Q. Some people are careful to burn or bury the nails cut, or at least to swipe them and remove them and not step on them, since there is danger. Does that apply also when they are the nails of a goy (found inside a kosher restaurant bathroom used by waiters)?
A. Mishna Berura (260: 6) mentions that indeed when the nails are moved from the location they fell, preferably to another room, they cannot do any harm. Melachim Omanaich (14: 18) quotes Horav Chaim Kanievsky Shlit'a that it does not apply to gentiles, as they also are not affected by the ruach ra'ah or the spirit of impurity that rest on one's hands after sleep.
Horav Shlomo Miller's Shlit'a opinion is to be lenient
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a