The corporation does not get a tax break.

They get the PR, and they get some leverage over the org they’re donating to. But, you know, the leverage is that they stop collecting money to the org, so if you refuse to give in the first place then…

It’s better to give to the charities of your choice without needing some other corp to effectively advertise and collect for them, but that seems unlikely. It probably is helpful that someone is out there advertising. It may be worth making that deal with the corp.