Before we jump into conclusions hastily, let's read closely what they're being accused of.
Treasury Secretary Scott Bessent said financial institutions cannot both support the Iranian regime and keep access to the U.S. financial system, adding that Treasury will keep working to "sever the Iranian regime's economic lifelines" and stop attempts to evade sanctions using digital assets.
The action is part of Operation Economic Outcast, a Treasury campaign launched in August to cut off financial entities that help Iran evade U.S. sanctions.
This is coming from the link provided by OP. They didn't involve themselves in illegal money in the sense that it was a stolen money, or conventional criminal activities. They processed payments from regions banned by the US.
Of course, processing transactions from sanctioned entities can itself be seen as an illegal activity under applicable sanctions laws. But it's not the same as saying that all the funds involved were stolen or gotten from criminal activities.
This is basically a geopolitical tossel between the US and other countries. The US is using its influence over access to its financial system to enforce their foreign policies on MEXC. Although, if MEXC wants to operate within the US jurisdiction, they should of course keep to their regulations and policies. But they're not like directly involved with the type of money laundry we're thinking of.