You could buy Silicone sheets.

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https://www.amazon.com/GUGUJI-Premium-Silicone-Dehydrator-Sheets/dp/B07FP3NXMZ/ref=pd_lpo_1?pd_rd_i=B07FP3NXMZ&psc=1

There are also Teflon sheets, which are smoother, but silicone is probably healthier.

https://www.amazon.com/Homey-Flexible-Resizable-Dehydrator-14x14-Inches/dp/B01EIWF25I/ref=sr\_1\_3?crid=21UBPTWJI3F1R&dchild=1&keywords=teflon+sheets+for+dehydrator&qid=1635081431&qsid=144-4740492-7405060&s=home-garden&sprefix=teflon+shee%2Cgarden%2C161&sr=1-3&sres=B01EIWF25I%2CB07VMH4V41%2CB0777SY2GY%2CB001PLE1O4%2CB07RV81PL8%2CB0728KWFV9%2CB078SGXTCK%2CB01MZ8ZNLV%2CB01640KAX6%2CB01MQEU057%2CB08NHL7KPF%2CB01MDTCKM0%2CB08MFF319Y%2CB00GSUXQAW%2CB08HGNW96K%2CB081ZJS81R%2CB07FP3NXMZ%2CB018QATE4I%2CB012CG8N26%2CB07W87NV3T&srpt=FOOD\_DEHYDRATOR

I was getting scuff marks from my glasses so my workaround was to use a silicone dehydrator sheet (link) cut to fit. It's thin silicone mesh so it still warms my cups, and it's grippy so it helps keep them from bouncing around as much while I'm pulling shots. It probably wouldn't help much for water stains, but you could probably do the same thing with a thin silicone placemat.