No source, but iirc the scientists applied a colored dot on the ants head. When they saw themselves in the mirror the started trying to remove it from their heads.
The issue you brought up about the mite is a bit orthogonal to this point. I can give you that the ant was concerned about the possibility of having a mite, and the point still remains that the ant thought it was on its own head only on basis of a reflected image of itself. (Compare to the alternative behavior: the ant tries to get the mite off the reflected image, never making any attempt to remove it from itself.)
it’s on wikipedia, with the same dead source https://en.wikipedia.org/wiki/Mirror_test?wprov=sfti1
EDIT: Working link to the paper (in some journal of science): https://www.udocz.com/read/are-ants-capable-of-self-recognit...
http://difusion.ulb.ac.be/vufind/Record/ULB-DIPOT:oai:dipot....