It took 12 posts before someone stated the obvious. Thanks!
The Oval Office reference was asinine to begin with.
Unless this is brinkmanship... the “dining room” would need to be convertible to a Sensitive Compartmented Information Facility or in other words a big Faraday cage “bubble” to prevent any transmission and a completely scanned group of senators with no devices, implants, or microphones. Period. Even doing all that would “transmit” a message.
There are secure rooms for large gatherings at the Eisenhower Executive Office Building which is part of the White House campus.