The factory-mounted screen protector is not bad, but (as with many TPU/plastic protectors) is prone to fingerprints and everything oily/greasy - so, yes, I have this too but for some time the protector was just fine.
I personally prefer glass screen protectors, which means the UV-glued variety for curved screens - preferably full kits which help fiddling with that ugly glue stuff, like the kits from Mowei and others...