It's the same spam we see on NIP-04. Anyone that just send tons of messages from random keys. The only difference is that relays can't do anything about GiftWraps. It must be resolved at the Client level.
Someone sent a bunch of GiftWraps to me a few months ago. Amethyst just ignored them all, deleted the event contents but kept the ids to avoid downloading them again.
We tested key aliases to hide the main pubkey of the user from the p-tag. You could give an alias to your friends and just download those messages instead. Something like a priority inbox. You can even rotate that key periodically to improve privacy.