We have a situation at work where developers working on a legacy (core) system are being pressured into using GOTO statements when adding new features into existing code tha
Maybe you can use the boyscout-pattern: Leave the place a little more clean than you found it. So for every featurerequest: don't introduce new gotos, but remove one.
This won't spend too much time for improvements, would give more time, to find newly introduced bugs. Maybe it wouldn't cost much additional time, if you remove a goto from the part, which although had to spend time understanding, and bringing the new feature in.
Argue, that a refactoring of 2 hours will save 20 times 15 minutes in the future, and allow faster and deeper improvements.