Sklenice or sklenička ('little glass') is made of glass (it's derived from sklo = 'glass'). There's also hrnek ('mug, cup') and šálek ('cup', or more like 'teacup'). Paper, styrofoam or plastic disposable cups are called kelímek.
Czech does not have any article, only demonstrative pronouns. It is not needed because, possibly, there are multiple glasses of different colours and you are telling which of them is hers. So it is clear you are speaking about a particular glass
So is "ta sklenice je jeji" acceptable or no?
Just trying to clarify whether "ta" is not needed or not correct.