There has been a lot of debate in the aviation maintenance community regarding the legality of attaching gopros etc. to aircraft with suction cups. Someone eventually wrote to the FAA chief counsel and asked.
"Another consideration, in the case of this type of equipment, is the applicability of the term "alteration". FAA Order 8110.3 7E, defines an alteration as "a modification of an aircraft from one sound state to another sound state". The use of suction cups, or other temporary methods of attachment (not including permanent mechanical attachments to the aircraft), would not be considered a modification to the aircraft."
That memo is about attaching it externally. Attaching it to an internal window is probably a non-issue.
I once had a security agent ask me to prove a GoPro was a camera because they didn't understand how there could be no screen or viewfinder. It was most frustrating because this was an area where they would have encountered it many times (lots of scuba divers).
"Another consideration, in the case of this type of equipment, is the applicability of the term "alteration". FAA Order 8110.3 7E, defines an alteration as "a modification of an aircraft from one sound state to another sound state". The use of suction cups, or other temporary methods of attachment (not including permanent mechanical attachments to the aircraft), would not be considered a modification to the aircraft."
https://mypilotpro.com/wp-content/uploads/2020/05/FAA-Camera...
But still, the aircraft is the the airline's property, not yours. If they tell you not do something to it, you don't get a choice in the matter.