so why is it that either 'este' or 'e' can be used here?
Because they are interchangeable in almost every context. "Este" is just that little bit more formal.
I thought "the table" was masa. I guess it's an idiom, where in Romanian you don't use the definite article in that phrase?
There is no definite article after a preposition usually.
You could take it as an idiom. A more detailed explanation is that you don't use the articulated version of "masă" here, because it's clear which table the speaker talks about.
You have the same phrasal feature in Italian: "da tavola"/"da tavolo". Perhaps it is a trait amongst Romance languages.
Actually in French you almost always need the article but it may be an exception since French has been highly influenced by German
here is an excellent answer for this https://forum.duolingo.com/comment/19086406