Do you think of dogs as unclean? Was I wrong for this?

Went for coffee with 2 ladies.
Doggy got a pup cup, but once finished he kept licking it and rolling it round on the floor. I picked it up and put it on the end of the table near me.

I noticed that one lady looked at the cup and cringed.

None of us were eating. Just drinking coffees from the Starbucks enclosed travel cups they serve drinks in. .

Was I wrong for doing that?