Is rense never used in this context?
No, "rense" would usually be used for clothes, and even then you can use "vaske".
Thanks! And so you would use Kokken vasker restauranten even if the cook doesn't use any water?
Water is no requirement for either "vaske" or "rense".
I think a better translation for "rense" would be "cleanse".
It has to be spotless!
How can you remember that vaske means cleaning?
Is “Kokken rydder restauranten” also a correct sentence, just not accepted as an answer here, because the verb “å rydde” is not introduced (yet)?
Not really. "Å rydde" means to tidy up/unclutter - and that's not exactly the same as cleaning.