I learned from my textbook that "no more than" meant "only", but I think, in the following picture, "no more than two" means "two or less". Which of the textbook and the sentence on the paper towel holder is wrong?

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They are both right, to a degree. The text on the paper towel dispenser could have "take only two towels", which, though technically not right, would be understood to mean "only 1 or 2".

If you write "Take only up to two", it would be correct.

So, your textbook is not 100% correct.

Similar:
◯　I can stay here no more than 5 days.
5日間以下。 (no more than 5 days = 5 days or less)
◯　I can stay here only 5 days.
5日間だけ (「本当はもっと長くいたいけど」の気持ちを表す)

Similar. Technically "only" is incorrect:
△　You can have only 5 beers a day.
◯　You can have up to 5 beers a day.
If you say "you can have only 5 beers", and someone drinks 4 beers, then they have violated your rules, since they did not have 5. But most people would understand the intention of "only 5 beers (or less)".