You can buy screens for TFT monitors to protect them. I don't think they are cheap but if its gonna save it getting ruined might be worth it.
I bought these tft cleaning wipes from pc world and they bring my tft up as good as new, but there weren't any sticky finger prints on them

I'm not sure sticky finger prints could break a tft but if kids are touching the screen there must be a real chance of killing some pixels.