What do you mean? What to check? If your coins are "dirty"? Every time I hear this, I can't help myself but wonder, who the f... is responsible to decide if a UTXO is "dirty"? Do we want Bitcoin to be decentralised or not? If yes, then there is no authority to judge. Bitcoin is freedom money, but if we fall into the "dirty" bitcoin trap, then Bitcoin is screwed and it will be used only via ETFs.

As far as XMR is concerned, the situation is different. Monero is a privacy coins which uses ring signatures and confidential transactions, making it essentially impossible to tell who paid who and how much. For me, this is fantastic, but for the authorities that desperately try to make people the "dirty" bitcoins narrative, monero is much worse because they can't control it. This is the reason why most centralised exchanges don't offer monero anymore. And this is why most services require KYC to allow you to trade Bitcoin for Monero.