system doesn't mess with any of the file handles passed to the child. If caller.pl is called interactively, so is ask_input.pl.

But why are you using -t? You need to get your answer from somewhere. You can't test if you're going to receive an answer from a terminal, so that's the last place you should check. You should base whether you prompt or not based on the presence or absence of the answer elsewhere (e.g. argument, config file).