@Andrea9 @Punam0
Punam
I would echo everything that Andrea has said (with the exception of most guests having separate insurance - that may not be that common?) but in any case - MOVE QUICKLY.
Do not rely on ABB to help resolve this - low odds and high inconvenience & effort are down that path. It sounds like you have a great guest and they are receptive to acknowledging/repairing the damage - so capitalize on that. Grab their willingness with both hands and come up with a solution fast. Each day that goes by - especially after the guests leaves - their willingness to contribute will fade, it's just part of human nature.
Personally I would accept that I will have to replace the lino at some cost - get a rough estimate figure and quickly decide on a contribution towards this to be paid for by the guest. Whether you claim on your own insurance for the damage - or just pay yourself - it is important to figure out an amount that you are happy with - but that isn't so large that it leaves a bad feeling with the guest. So whatever that may be - discuss it with the guest and ask them to pay you NOW.
Offer them a brief written letter stating that, as a result of the damage caused to the floor, you are content to accept XX amount as their contribution towards repair & replacement of the flooring, and this payment ends their liability to you and the matter will not be taken further. And that you are appreciative of their willingness to contribute etc. etc... Dated and signed by you and them.
Hopefully then it can all be forgotten and your review and the rest of their stay will not suffer as a result of any bad feeling. And you can always buy a bigger bathroom rug to help with cover ups while you decide on how to proceed. 🙂
Hope this helps,
Rachael