How do you put irrelevantly in a sentence?

Answer 1

You don't. Something is "irrelevant" or "useless" maybe, but irrelevantly (much like "irregardlessly") is not a word.

Irrelevantly is not only a word but it is an adverb, irrespective of what you've heard. Irrelevant is an adjective. The normal way to change an adjective into an adverb is to add ly to the end. Here is your example sentence.

He broke the jar of mayonnaise, with the contents spilling all over the floor and then irrelevantly replaced the lid.