it occurred to me that if the double-quotes are at all valuable in and of themselves, and happen to just be a problem for the recieving program, you might want to consider translating them to something other than an empty string, i.e.:
$string =~ tr/"/'/d;
of course the problem here being that you run the risk of changing the meaning of the string in other ways
Following on from this point.
Check the docs on the software which is treating the " as a line ending character. It might have an escape syntax for the " and other characters it has special behaviours for.