The client is clearly provoking a conflict, ignoring all suggested options of settlement. Earlier this client said that all information, violating the user agreement had been removed, but the investigation found out that, on the contrary, there is much more such information now. All further discussions of this issue will be held solely with the client and only after eliminating all negative effects.
You have no right to keep the funds regardless of what "information" the customer published. You can terminate your service to the customer if they violated the user agreement but you need to return their money.