Will my charity get penalized?

My small charity is receiving numerous requests from companies that want to put our logo on their webpage and say that x% of their profits are going to our charity. The number of companies requesting this is too much for my small team to handle.

Is it ok to allow them to the use our logo in a way that complies with IRS and state laws (CA and IL specifically)? We are otherwise not actively engaged with these companies and don't have a way to verify if they are actually donating x% of profits.

Thank you for any advice you can provide!