Try to think in terms of the Romanian language.
Here, 'pe masă' means 'on a table'. Here, we are not talking of a specific table.
It makes perfect sense to use 'pe masă'. But going word-to-word, it translates to 'on table' which is not very grammatically sound. So there comes 'the' in the translation.
If we were talking of a specific table, only then we would use 'pe masa'. The translation would still remain 'on the table'
Hope I helped! :))
i would translate and have translated the sentence(!!) as : to appear at the table.... in english to appear sounds like a fairy appearing at the table and with her wand she conjures a cake on the table...heheh!!! i suppose the sentence means that someone has (finally) appeared at the table for dinner after having been called many times to come for dinner!!!!