Q. This might be the easiest question, but if someone touches something impure after wudu, is the wudu invalid? IE: In the morning, when one wakes up and goes to ghusl he/she will turn on the shower handle to start the water with impure hands. If he/she touches the shower handle AFTER the ghusl and didn’t realize or forgot he/she had to clean it to make it pure, is the ghusl to be re-performed? Or should we do wudu? Or is this some sort of Makrooh ghusl I’ve yet to learn about…
A. Under general circumstances, touching something impure has nothing to do with wudhu. For example, a person touching blood, puss, changed a child’s diaper despite the hand becoming soiled in such an exchange,  etc. would not break wudhu. However, if one does touch something that is impure, or or for that manner says something foul, or attempts to play mind games for deceptive purposes, upon lying,  being provocative when uncalled for, etc. then making a fresh wudhu would be ideal. (This answer is for hanafees.) (Please see noor ul idah)

The ghusl had been completed despite the touch of impurity. Wuzu would also be viewed as complete. Since it is after the ablution and ghusal that the impurity was touched, all you had to merely do was wash the impurity off and be considered clean. (hanafee). Under ideal conditions, a fresh wuzu would be ideal as a result of touching filth. (Please see noor ul idah)

Had the impurity been that of and its spread upon the hand was beyond the dimension of a dirham, then this would not fall into the catorgory of not merely makrooh, but such a ‘touching’ would warrant a total washing off of the impurity.  Salah would not be accepted with an impurity which falls in the category of najasathi ghalizah which has a spread of a dirham upon the body. If by ‘impure’ you meant that you hands was merely not clean, but not as a result of najasathi ghalizah but najasati kafifa, then of course there would be no to worry about in this given situation.

Allah Certainly knows best.