I had issues with flys sucking of the paint from the paper too when I swatched a new water colour set. I have never seen insects “eating” paints before nor did that happen to me after this event.
It is weird that the insects got into your pallet. What kind of pallet do you use? I have go a Mijello pallet for my gouache paints that can be closed tightly. But I know that some bugs can squeeze trough the tiniest spaces which got me worried a bit. Maybe a plastic bag a seal the pallet away like the others suggest as well could help you.
Of course you should also check how they got into your house at first place. There might be sprays or something to keep all kinds of bugs out of your house.