Let's look at three homophones: peak, peek, and pique. Peak is a topmost point, such as a mountain peak, or to reach that point:

We're sort of at peak demand right now.

A peek is a glance or a quick look, like you do with the unwrapped Christmas presents at the bottom of your loved one's closet. It can also mean to glance or to peer at. It's frequently paired with sneak, which can lead you to use the incorrect peak:

Residents take a peek at bike and pedestrian safety plans Yellowstone Offers Sneak Peek Of New Visitor Center

Finally, pique is to upset or excite someone. You will sometimes see peek one's interest for pique one's interest, but don't be fooled. If you're piquing someone's interest, you are exciting their interest not taking a quick look at it:

If that doesn't pique your interest, you can leave (but I'm keeping your shoes).

Here's your mnemonic device: