The bank wants to raise money for a local organization. The plan is to allow customer to donate and the bank will match $1 for $1 up to$1,000. My compliance senses are blinking for numerous reasons.... internal controls, do we need to give donation receipts for taxes?, is there reputational risk? Thoughts?

"A local organization"? If it is not the one I support, I would be miffed.

Is there any compliance or law restrictions?

Not really, it is all about customer relations. So, if a thousand people show up and pledge $1,000, you guys are really going to fork out $1MM? As far as tax consequences for the bank and the contributors and documentation requirements, talk to your CPA firm.

The only concerns I can think of is if the organization supports a limited section of the community, or conversely excludes (or makes it difficult) to include all, or for the customer side that you have customers that support other similar groups who want their fair share.
Our bank tried it once, and there was support, also requests to the branch management why their organization was excluded. It was a one time shot - caused more animosity that relief.