If it's 勝手に食べといて！, it can also mean "Help yourself while you can!", but since it says 人のものを, it's so obvious to us that it's a complainment, and means "What is it after you've eaten something belongs to others[(or likely) me]!". Something like 何なのよ is implied after it.
You're right that the といて here is a colloquial contraction of ておいて.
「～～ておいて！」 is actually a pretty common phrase for giving a complaint or blaming someone for doing/saying something that contradicts what they did earlier.
「Verb + ておいて！」, ending with a te-form, literally is:
"You have done (Verb), and ~~~!" / "~~~, while you've done (Verb)!"
with the main clause (i.e. the "~~~" part) left unsaid.
Your sentence could mean something along the lines of:
You've eaten my food without asking me (, and now what are you saying?)!
「人のものを勝手に食べといて（、よくもそんなことが言えるな / できるな）!」
You've eaten my food without asking me (, and now how dare you say that / do that?)!