Here are, in no particular order, a couple of solutions to consider.
Before usage I recommend creating a backup copy of any .txt file that you're going to try them with. These scripts can potentially cause loss of valuable data if not used carefully.
If you have any concerns regarding assignment of the correct filepath to either;
- The txtFilePathvariable in Solution A
- The txtFilePathproperty in Solution B
then replace either of those lines with the following. This will enable you to choose the file instead.
set txtFilePath to (choose file)
Solution A: Shell out from AppleScript and utilize SED (Stream EDitor)
on removeMatchingLinesFromFile(findStr, filePath)
  set findStr to do shell script "sed 's/[^^]/[&]/g; s/\\^/\\\\^/g' <<<" & quoted form of findStr
  do shell script "sed -i '' '/^" & findStr & "$/d' " & quoted form of (POSIX path of filePath)
end removeMatchingLinesFromFile
set txtFilePath to "Macintosh HD - Data:Users:crelle:Desktop:TestDelta.txt"
set lineOfTextToDelete to "The quick brown fox jumps over the lazy dog."
removeMatchingLinesFromFile(lineOfTextToDelete, txtFilePath)
Explanation:
- The arbitrarily named - removeMatchingLinesFromFilesubroutine / function contains the tasks necessary to meet your requirement. It lists two parameters;- findStrand- filePath. In its body we "shell out" twice to- shby utilizing AppleScript's- do shell scriptcommand.
 - Let's understand what's happening here in more detail: - 
- The first line that reads; - set findStr to do shell script "sed 's/[^^]/[&]/g; s/\\^/\\\\^/g' <<<" & quoted form of findStr
 - executes a - sedcommand. The purpose of this command is to escape any potential Basic Regular Expression (BRE) metacharacters that may exist in the given line of text that we want to delete. Utlimately it ensures each character in the given string is treated as a literal when used in the subsequent- sedcommand - thus negating any "special meaning" the metacharacter has.
 - Refer to this answer for further explanation. Essentially it does the following: - 
- 
- Every character except ^is placed in its own character set[...]expression to treat it as a literal.
- Note that ^is the one char. you cannot represent as[^], because it has special meaning in that location (negation).
 
- Then, ^chars. are escaped as\^.
- Note that you cannot just escape every char by putting a \in front of it because that can turn a literal char into a metachar, e.g.\<and\bare word boundaries in some tools,\nis a newline,\{is the start of a RE interval like\{1,3\}, etc.
 
 
 - Credit for this SED pattern goes to Ed Morton and mklement0. - So, given that the string assigned to the variable named - lineOfTextToDeleteis:
 - The quick brown fox jumps over the lazy dog.
 - we actually end up assigning the following string to the - findStrvariable after it has been parsed via the- sedcommand:
 - [T][h][e][ ][q][u][i][c][k][ ][b][r][o][w][n][ ][f][o][x][ ][j][u][m][p][s][ ][o][v][e][r][ ][t][h][e][ ][l][a][z][y][ ][d][o][g][.]
 - As you can see each character is wrapped in opening and closing square brackets, i.e. - [], to form a series of bracket expressions.
 - To further demonstrate what's happening; launch your Terminal application and run the following compound command: - sed 's/[^^]/[&]/g; s/\^/\\^/g' <<<"The quick brown fox jumps over the lazy dog."
 - Note When running the aforementioned compound command directly via the Terminal the - sedpattern contains less backslashes (- \) in comparison to the pattern specified in the AppleScript. This is because AppleScript strings require any backslash to be escaped with an additional backslash.
 
- The second line reading; - do shell script "sed -i '' '/^" & findStr & "$/d' " & quoted form of (POSIX path of filePath)
 - executes another - sedcommand via the shell. This performs the task of finding all instances of the given line of text in the file and deletes it/them.
 - 
- The - -ioption specifies that the file is to be edited in-place, and requires a following empty string argument (- '') when using the BSD version of- sedthat ships with macOS.
 
- The - '/^" & findStr & "$/d'part is the pattern that we provide to- sed.
 - 
- The - ^metacharacter matches the null string at beginning of the pattern space - it essentially means start matching the subsequent regexp pattern only if it exists at the beginning of the line.
 
- The Applescript - findStrvariable is the result we obtained via the previous- sedcommand. It is concatenated with the preceding pattern part using the- &operator.
 
- The - $metacharacter refers to the end of pattern space, i.e. the end of the line.
 
- The - dis the delete command.
 
- The - & quoted form of (POSIX path of filePath)part utilizes AppleScript's- POSIX pathproperty to transform your specified HFS path, i.e.
 - Macintosh HD - Data:Users:crelle:Desktop:TestDelta.txt
 - to the following POSIX-style path: - /Macintosh HD - Data/Users/crelle/Desktop/TestDelta.txt
 - The - quoted formproperty ensures correct quoting of the POSIX-style path. For example, it ensures any space character(s) in the given pathname are interpreted correctly by the shell.
 
 
 - Again, to further demonstrate what's happening; launch your Terminal application and run the following compound command: - sed -i '' '/^[T][h][e][ ][q][u][i][c][k][ ][b][r][o][w][n][ ][f][o][x][ ][j][u][m][p][s][ ][o][v][e][r][ ][t][h][e][ ][l][a][z][y][ ][d][o][g][.]$/d' ~/Desktop/TestDelta.txt
 
 
- Let's understand how to use the aforementioned - removeMatchingLinesFromFilefunction:
 - 
- Firstly we assign the same HFS path that you specified in your question to the arbitrarily named - txtFilePathvariable:
 - set txtFilePath to "Macintosh HD - Data:Users:crelle:Desktop:TestDelta.txt"
 
- Next we assign the line of text that we want to find and delete to the arbitrarily named - lineOfTextToDeletevariable:
 - set lineOfTextToDelete to "The quick brown fox jumps over the lazy dog."
 
- Finally we invoke the custom - removeMatchingLinesFromFilefunction, passing in two required arguments namely;- lineOfTextToDeleteand- txtFilePath:
 - removeMatchingLinesFromFile(lineOfTextToDelete, txtFilePath)
 
 
Solution B: Using vanilla AppleScript without SED:
This solution provided below does not utilize the shell, nor SED, and produces the same desired result as per Solution A.
property lineOfTextToDelete : "The quick brown fox jumps over the lazy dog."
property txtFilePath : alias "Macintosh HD - Data:Users:crelle:Desktop:TestDelta.txt"
removeMatchingLinesFromFile(lineOfTextToDelete, txtFilePath)
on removeMatchingLinesFromFile(findStr, filePath)
  set paraList to {}
  repeat with aLine in getLinesFromFile(filePath)
    if contents of aLine is not findStr then set paraList to paraList & aLine
  end repeat
  set newContent to transformListToText(paraList, "\n")
  replaceFileContents(newContent, filePath)
end removeMatchingLinesFromFile
on getLinesFromFile(filePath)
  if (get eof of filePath) is 0 then return {}
  try
    set paraList to paragraphs of (read filePath)
  on error errorMssg number errorNumber
    error errorMssg & errorNumber & ": " & POSIX path of filePath
  end try
  return paraList
end getLinesFromFile
on transformListToText(ListOfStrings, delimiter)
  set {tids, text item delimiters} to {text item delimiters, delimiter}
  set content to ListOfStrings as string
  set text item delimiters to tids
  return content
end transformListToText
on replaceFileContents(content, filePath)
  try
    set readableFile to open for access filePath with write permission
    set eof of readableFile to 0
    write content to readableFile starting at eof
    close access readableFile
    return true
  on error errorMssg number errorNumber
    try
      close access filePath
    end try
    error errorMssg & errorNumber & ": " & POSIX path of filePath
  end try
end replaceFileContents
Explanation:
I'll keep this explanation brief as the code itself is probably easier to comprehend than Solution A.
The removeMatchingLinesFromFile subroutine essentially performs the following with the aid of additional helper functions:
- read's the contents of the given- .txtfile via the- getLinesFromFilefunction and- return's a list. Each item in the returned list holds each line/paragraph of text found in the- .txtfile content.
 
- We then loop through each item (i.e. each line of text) via a - repeatstatement. If the- contentsof each item does not equal the given line of text to find we store it in another list, i.e. the list assigned to the- paraListvariable.
 
- Next, the list assigned to the - paraListvariable is passed to the- transformListToTextfunction along with a newline (- \n) delimiter. The- transformListToTextfunction returns a new string.
 
- Finally, via the - replaceFileContentsfunction, we- open for accessthe original- .txtfile and over- writeits contents with the newly constructed content.
 
Important note applicable to either solution: When specifying the line of text that you want to delete, (i.e. the string that is assigned to the lineOfTextToDelete variable), ensure each and every backslash \ that you may want to search for is escaped with another one. For example; if the line that you want to search for contains a single backslash \ then escape it to become two \\. Similarly if the line that you want to search for contains two consecutive backslashes \\ then escape each one to become four \\\\, and so on.