It's your choice whether or not to give them gifts. You don't need permission to stop. But how old are these kids? Are they young enough that you're just punishing them for their parents' neglect to teach them these things? Also, don't hold the grudge too long, they are kids and should be given a 2nd chance eventually if you do stop giving gifts.
I do think this is a good point. At least, maybe you (general) won't having a gifting rel
ationship with them, but you could still have a positive emotional rel
ationship with them, maybe as they get older and more independent. Giving all those unacknowledged gifts really soured my opinion of my nieces and nephew and their parents (not unreasonably). Once I stopped sending the gifts, and a little time had passed, I felt a lot better about them. I wasn't investing as much time, effort, and money into them, so they had a much lower bar to hit for me to feel okay with the rel
ationship.
This sounds like I'm excusing them for not thanking me; I'm not. I'm just saying, I was unhappy with the lack of balance in the rel
ationship, and since they wouldn't reach "up," I dropped "down," if you see what I mean, and I feel like a new balance has been achieved, which I'm content with. Now that the kids are getting older and starting to go to college, I hope maybe I can have a more adult-to-adult emotional rel
ationship with them. I have no intention of sending them gifts again any time soon, though. I wouldn't rule it out forever and ever, but we're going to have to get a lot closer, and they'll have to show me that they've matured a lot more, before I try that again. But I don't think ill of them still.
It's hard when the kids are young and their house just seems to be a black hole, except for when they or their parents demand more.

I've never encountered that situation personally but it would be really unpleasant. I think you have to figure that you're probably not really "punishing" the kids--they will most likely get gifts and necessities from other people, like their parents. If you really suspect they are
not getting anything, if you don't send it, there are other strategies you can try, but I think that's a different situation.