The task can be done with a batch file with following command lines:
@echo off
setlocal EnableExtensions DisableDelayedExpansion
for /F "delims=" %%I in ('dir "%~dp0*-min.*" /A-D /B /S 2^>nul') do (
    set "FullFileName=%%I"
    set "FileNameOnly=%%~nI"
    set "FileExtension=%%~xI"
    setlocal EnableDelayedExpansion
    if /I "!FileNameOnly:~-4!" == "-min" ren "!FullFileName!" "!FileNameOnly:~0,-4!!FileExtension!"
    endlocal
)
endlocal
The twice used negative value -4 must match with the length of the string to remove from the end of the file name left to the file extension. The string -min has a length of four characters which is the reason for using here twice -4.
The command DIR executed by a separate command process started by FOR in background with %ComSpec% /c and the command line between ' appended as additional arguments outputs also file names like Test-File!-min.x.pdf with full path. For that reason the IF condition makes sure to rename only files of which file name really ends case-insensitive with the string -min like Test-File!-MIN.pdf.
Read the Microsoft documentation about Using command redirection operators for an explanation of 2>nul. The redirection operator > must be escaped with caret character ^ on FOR command line to be interpreted as literal character when Windows command interpreter processes this command line before executing command FOR which executes the embedded dir command line with using a separate command process started in background.
The code works even for files of which fully qualified file name (drive + path + name + extension) contains one or more exclamation marks because of delayed variable expansion is enabled only for the command line which finally renames a file.
The file renaming task can be done faster with permanently enabled delayed variable expansion as long as no file contains anywhere one or more ! in its fully qualified file name.
@echo off
setlocal EnableExtensions EnableDelayedExpansion
for /F "delims=" %%I in ('dir "%~dp0*-min.*" /A-D /B /S 2^>nul') do (
    set "FileNameOnly=%%~nI"
    if /I "!FileNameOnly:~-4!" == "-min" ren "%%I" "!FileNameOnly:~0,-4!%%~xI"
)
endlocal
This code does not work for renaming Test-File!-MIN.pdf to Test-File!.pdf because of ! in file name.
To understand the commands used and how they work, open a command prompt window, execute there the following commands, and read the displayed help pages for each command, entirely and carefully.
- call /?... explains- %~dp0... drive and path of argument 0 which is the full path of the batch file which always ends with a backslash. It is concatenated with the wildcard pattern- *-min.*for that reason without an additional backslash.- %~dp0can be removed to run DIR on current directory and all its subdirectories instead of batch file directory and all its subdirectories.
- dir /?
- echo /?
- endlocal /?
- if /?
- ren /?
- set /?
- setlocal /?
See also this answer for details about the commands SETLOCAL and ENDLOCAL.