Removing water marks from fine furniture!

[Lovepancakes]

I'm a bit worried as a visiting child put a cup on a piano which isn't ours and its left a big mark.

I just tried mixing ash and mayonnaise and testing it on a less good piece of furniture with a similar Mark. It didn't work but I didn't read Google properly as it said to leave it overnight!

I'm wondering whether to buy a cloth from Lakeland that claims to work and has 4 out of 5 star reviews unless anyone thinks I can manage by a homemade method?!

Thanks so much for any tips

You are amazingly kind. I'll see if I can find very fine wire wool tomorrow but a bit sad I will otherwise miss your antiques visit which was so thoughtful of you as we are going away. That's such a lovely and thoughtful idea though.

Where Can one buy polishes in different hues?