I have a recipe from my grandma for "cheese straws". It says to "Rub cheese through a wire sieve". I grated the cheese on the smallest holes & nada

Rub it through the finest strainer you have. Scrape it off the back side with the top edge of a butter knife. Alternatively, use a cheese grater. These are designed to grate Parmesan cheese very finely. It's likely that your recipe for cheese straws calls for Parmesan cheese.

I've only seen recipes calling for grated cheese. I would have grated the cheese on a metal 4-sided grater on the side with the small tear-drop shaped openings, not the smallest holes.