@Kashif14 The host surely knows her claim is ridiculous. Only an absolute idiot would throw away a whole sofa over a superficial mark. What she's hoping for is that when you decline the charge (and of course you should), Airbnb's insurance scheme ("AirCover") will take over and buy her a brand new sofa to replace her somewhat worn-out old one. Unfortunately, the only way to get there is to stick the guest into the middle.
This appears to be a lower-end sofa that would be just as usable with a slipcover to conceal the mark. Those run between $100-150, which would be a fair amount to offer.