You're not supposed to use that. It can cause chatter in the rack. The seals are engineered for use with the Honda fluid as well. Even the generic manufacturers normally make a Honda-compatible fluid, which is OK to use. It says Acura/Honda right on the bottle, and usually only costs a dollar or so more that the generic stuff.
Also, what you are wiping your fluid with when checking levels isn't worth thinking about this much. As long as the stick is clean when you jam it back in the hole, it's all good. Just like she said.
. Sometimes I just use my fingers, and wipe them on my pants when I've finished.