"Sometimes they eat from the old plates."
Translation:Někdy jedí z těch starých talířů.
I did not insert "těch" and I got it right. Does it mean that the presence or absence of the article does not make a real difference?
Czech hasn't got any articles. These are demonstrative pronouns and do not correspond exactly to English definite articles. They certainly do make a difference and in most sentences you can't leave them out when they are needed. Here you can theoretically leave "těch" out, when it is clear from the context, which old plates you have in mind.