As said, pay absolutely nothing, sign absolutely nothing in response to this not ever.
There are companies out there that like to try their luck with things like this – an old debt of mine was once bought for 'pennies on the pound' – sold by a company that was never allowed to sell it, and the company was trying to get me to pay it even though the whole thing was in fact 'statute barred'. As soon as I pointed that out to them in a letter and told them that under no circumstances was I ever going to pay they backed off and dropped it completely.
There was a financial advisor at work that helped, but I also found a lot of information at TPUC – the peoples united community, although it seems that the particular stuff which helped me has been dropped in favour of well – more extreme action.
If they are accusing you of something it has to be done in a way that is legally watertight – suggest as such and most illegitimate operators will crumble.
Don't apologise, get advice and make your stand in a letter – legally.
Don't drop the game – just change the gfx! Tell then that you have ceased using the 'offending' material.