Q. If you had a neggel vasser cup out with water and you accidentally dipped your finger in it or your pet dog drank from it, does the whole cup need to be emptied or is it sufficient to merely add some new water to it?
A. Dipping your finger in water, if you didn't have any intention of cleaning it, does not affect the water to be used for Netilas Yodaim.
Regarding water that a dog drank from it, Shulchan Aruch (O.H. 160: 4) permits it to be used for Netilas Yodaim. Mishna Berura (23) quotes Poskim that it depends on the animal and dogs are excluded. He mentions that Chaye Adam allows in need.
Horav Shlomo Miller's Shlit'a opinion is that for Neigel Vaser after one wakes up, it can be used.
Adding some drops of water, is only effective when dealing with wine to be used for Kiddush, when someone drank from that wine. and not in our case.
Rabbi A, Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit'a