Xion

They will if you don’t reply to their message.
You are obligated to respond.
You either contact a lawyer or you reply with a modificated version of there message.

Did you receive a cease and desist letter?
If so, by signing it you would admit to doing what they claim.
But if you change the letter from “I will never do it again” to “I will never do it and never did it”, you admitted to nothing.
In most cases, those firms don’t want to go to court. They mostly prey on the scared people that pay without a fight.
This is not a legal advice!