Assuming the quotes are correctly balanced and there are no escaped quotes, then it's easy:
result = subject.gsub(/a(?=(?:[^"]*"[^"]*")*[^"]*\Z)/, '')
This replaces all the as with the empty string if and only if there is an even number of quotes ahead of the matched a.
Explanation:
a        # Match a
(?=      # only if it's followed by...
 (?:     # ...the following:
  [^"]*" #  any number of non-quotes, followed by one quote
  [^"]*" #  the same again, ensuring an even number
 )*      # any number of times (0, 2, 4 etc. quotes)
 [^"]*   # followed by only non-quotes until
 \Z      # the end of the string.
)        # End of lookahead assertion
If you can have escaped quotes within quotes (a "length: 2\""), it's still possible but will be more complicated:
result = subject.gsub(/a(?=(?:(?:\\.|[^"\\])*"(?:\\.|[^"\\])*")*(?:\\.|[^"\\])*\Z)/, '')
This is in essence the same regex as above, only substituting (?:\\.|[^"\\]) for [^"]:
(?:     # Match either...
 \\.    # an escaped character
|       # or
 [^"\\] # any character except backslash or quote
)       # End of alternation