"simply to attach a statement that the TP knew about this"

The IRS tells you what to do at the link I gave.

"So a new entity was formed (the why is not material). The old cc machine with the original ein was used for the rents."

Did you read that info?

"If you shared your credit card terminal with another person or business:

If you shared your credit card terminal with another person or business, your Form 1099-K will include payment card transactions belonging to the person or business that shared your terminal, in addition to your own payments. Where required, you should file and furnish the appropriate information return (e.g., Form 1099-K or 1099-MISC) for each person or business with whom you shared a card terminal. The information return should include the total payment card transaction amount in addition to any other income belonging to the other person or business. You should retain records of payments issued to each person or business sharing your terminal, including but not limited to shared terminal written agreements and cancelled checks."

As I noted, 1099-Misc Box 1 is for Rents. That means your old entity, the owner of the Terminal, would issue a 1099-Misc to the landlord entity, because I am assuming the old entity paid over the funds from the terminal processing to the new entity, since it was their Rent.

And now the old entity has money In and money Out, and has done the required reporting.

It's not just a statement, in this case, if that is what you intend to do.