I'm glad you're involved enough to know this and care about it. I'm 44 and have no kids, so take this with a huge grain of salt... But I'd probably let my kid keep it. At 16 you can just sit them down and have a talk with them about it. (And it sounds like you have.) Let them know this means his friend's family has money that he does not, and you do not.
Let him know that he shouldn't take advantage of his friend's cavalier attitude and kindness, nor should he let his friend's familial wealth pressure him. He should appreciate this, but not expect it, or feel guilty about it. And let him know this is a complex thing, and if they need to talk about it, it's better they approach you to talk about it early rather than late.
Underscore that this is squarely his friend's parents money, not his friend's. It can come and go at any time, and that's okay. Value the friendship more than the money, and if that changes, don't accept such gifts.
My folks would invite a cousin my age over for the night before Christmas when we were all in our mid teens. The next morning he would things like clothes, shoes, and an electric razor; things a young guy needs. My folks were not rich, just lower middle class and able to help out. It's a different situation than you're in. But if this family of your child's friend has money and wants to spread the love and is capable of doing so in an adult and healthy way, I personally think 16 is an age at which someone can begin to deal with the complex dynamics of monetary differences.
You know your kid better than us strangers online. And remember, they also have you on their side. Growing up is going to be difficult anyway. Just be there for them when they need it, and they'll probably be fine.
Edit: And also maybe get to know the other set of parents better. Explain to them you're appreciative of their kindness, and so does your son, but that your concern is just that you don't want it to create an awkward dynamic between your children in the future. Again 16 is young adult, but still a kid, so I understand your concern. They probably will to.
I abandoned Twitter for Mastodon a few months after Musk bought Twitter. I figured I'd keep the account around to DM people who there, just in case my need to do so arose. Then I kinda forgot about it. Cut to a few months ago I sent a message to someone on a different service. I knew they were doing a project, but I politely asked them "hey, do you have the interest and time to do xyz?"
They said "I'm sorry, I'd normally love to, I'm just really busy right now and don't have the time; you probably know I'm doing ABC myself." And that was legit. But they added "Also, you should know I generally don't work with people who have Twitter accounts anyway, for future reference."
Initially I was "But wait, I don't USE it..." But I took a few minutes to think about it. I mean, he wasn't wrong. I DID have an account at the Nazi bar... And I don't use it. It just lends my name to the service for no benefit to me. And that's why I decided to download my data and delete my account. Sometimes calling people out (in a helpful way,) can be a positive.
And that, dear reader, not necessarily the person I'm replying to but you reading this, is now me reminding you that you can delete your Twitter account and stop supporting the Nazi bar.