My wife wears cosmetics at home and on occasions, traces of this might remain even after ablution – wudhu. Does this invalidate her prayer and if so, what should she do about the untold number of prayers which she might also have offered in similar circumstances.

As long as these traces of make-up do not prevent water reaching her skin, there is
no problem. If however the grease in the make-up prevented water reaching the skin of her
face during wudhu, she will have to offer compensatory – qadha – for all the prayers she might have missed.