A paper straw is three materials, and a compostability claim has to cover all three.
Paper is not the whole straw
The straw is paper, printing ink and adhesive. Certification applies to a finished article, so a certified paper glued with a conventional adhesive does not produce a certified compostable straw.
Ask whether the certificate covers the finished straw or only the paper stock. The answer is often the second one.
Industrial is not home
Certified compostable means industrially compostable unless the certificate specifically says home compostable. Industrial composting runs hotter and for longer than any garden heap.
If your customers have no access to industrial composting, the straw goes to landfill like any other paper. That is worth knowing before it goes on your packaging.
Then there is the wrapper
An individually wrapped straw is a pack, and the wrapper is part of it. A certified straw in a conventional plastic wrapper is not a compostable product.
Specify a matching certified wrapper, or do not make the claim about the wrapped item.
What to put on your packaging
Only what the certificate supports, and name the standard. Vague words like eco-friendly and biodegradable carry no defined meaning and attract exactly the attention you do not want.
We supply the documentation with the order so the accurate claim is easy to write.