Not too sure about 'peppermint' exactly. But I believe they can eat mint leaves. Give it in a very tiny portion at first though, if you are uncertain. They are herbs, so it should be fine.
But you need to wash the mint leaves thoroughly! They could have some sort of chemicals on them or bugs or something nasty. So scrub scrub scrub with some slightly warm water, leave to dry, and then give it to 'em~
BUT! If you're still uncertain don't try at all. I'm not an expert, sooo. . .yeah~ I just know a few of my friends who have tried mint leaves and their birds are just fine.