there is nothing in this sentence to indicate the past tense. It would seem to me that, 'they finish eating', should be acceptable
If there was more context to the sentence then 'they finish eating' might be acceptable. As it is, 'they finished eating' should be the correct translation. The present tense would require more context in this example rather than the past tense.
Why "they finish to eat" is wrong?
Some english speakers might not feel comfortable using the infinitive with "to" instead of the gerundive with "-ing", but technically that should be correct. "Finish" or "finished" are both possible
because that is not gramatically correct in english
They do but I don't.
I never do