May Allah reward you greatly. When one washes his feet in wudu do they need to be completely free of dirt, because sometimes dirt comes on the foot and stains it and it is hard to get off unless you rub the skin and this may damage it. Wa salam alaikum wr wb

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If the said dirt prevents water from reaching the skin, then it should be removed because it is one of the conditions of ablution that water must reach the entire limb that must be washed in ablution. If it is difficult to remove the dirt and this causes harm then it is not an obligation to remove it especially if it is tiny. This is in inference with what the scholars said that one whose bone is sutured with an impure suture or that his injury was splinted with an impure suture, then one is not obliged to take it off due to the harm this could lead to.

Moreover, some scholars –like Ibn Taymiyyah –are of the view that little dirt which prevents the water from reaching the skin, does not constitute a problem if not removed, even if removing it can easily be done. Therefore, any small amount, like blood or dough and the like, that prevents the water from reaching any part of the body, it does not constitute an obstacle in inference with what is under the nail.

As regards the dirt that does not prevent water from reaching the skin, then it is not an obligation to remove it when performing ablution. 

Allaah Knows best.