Exchanges will never tell you anything about it. More precisely, the customer support staff you get to talk to have no idea, and the little information they know, they aren't going to share with you. I did an experiment some time ago where I asked support agents of CEXs what they consider "tainted" bitcoin and what kind of coins they reject. As expected, I didn't discover anything useful besides the usual generic replies of how the exchange is interested in protecting all clients and their money and only exists to serve us, their loyal customers .

In essence, they want you to deposit your coins. If their "research" discovers anything wrong with them, they will let you know by freezing your account and asking for more information.

You can still get caught in the middle of it if you use centralized exchanges that make you play by their rules. Then, if you want your money, you'll have to comply. The right thing to do is to not deposit to CEXs at all.