Could be...but I believe it's a Presidential Service Badge
The Presidential Service Badge is a badge of the United States military issued to service members who serve as full-time military staff to the President of the United States. Such personnel are stationed at the White House and should not be confused with the senior military officers of the United States Department of Defense who advise the President but are not assigned as direct Presidential aides. Each badge is stamped with a unique serial number which, when issued, associates that badge with a specific individual.
The Presidential Service Badge is recorded in the awardee's military service records and is authorized for wear as a permanent decoration.
Recipients are the only Americans authorized to wear the "Presidential Seal or Coat of Arms" on their uniforms and civilian clothes.
Paratrooper was the first thing I thought when I saw it, too.
Edit: If they're talking about the thing on his hat, I don't think it matches the one with the parachute, but I still really don't know what either seal means.
USPA?
https://www.uspa.org/portals/0/Images/logo_flaticon.png
Could be...but I believe it's a Presidential Service Badge
The Presidential Service Badge is a badge of the United States military issued to service members who serve as full-time military staff to the President of the United States. Such personnel are stationed at the White House and should not be confused with the senior military officers of the United States Department of Defense who advise the President but are not assigned as direct Presidential aides. Each badge is stamped with a unique serial number which, when issued, associates that badge with a specific individual.
The Presidential Service Badge is recorded in the awardee's military service records and is authorized for wear as a permanent decoration. Recipients are the only Americans authorized to wear the "Presidential Seal or Coat of Arms" on their uniforms and civilian clothes.
https://www.rollofhonor.org/public/htmldetails.aspx?Cat=badge&EntID=81#:~:text=The%20Presidential%20Service%20Badge%20is%20recorded%20in%20the%20awardee's%20military,their%20uniforms%20and%20civilian%20clothes.
So NOT paratrooper related?
Paratrooper was the first thing I thought when I saw it, too.
Edit: If they're talking about the thing on his hat, I don't think it matches the one with the parachute, but I still really don't know what either seal means.