A Cutts Compensator on my Thompson M1A1... Weird?

Can anyone help me to identify why my Thompson M1A1 is fitted with a Cutts Compensator?

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I was always taught that the Cutts Compensator was never fitted to the M1 or M1A1, however I now find that I may have been put wrong.

 

Just a Little more info for you if it at all helps:

THOMPSON M1A1 .45 SUBMACHINE GUN WITH CUTTS COMPENSATOR, FULLY FUNCTIONING, DATED 1943.
Serial number #439206.
Barrel marked “P”.
Left side of receiver stamped “Thompson Submachine Gun, Caliber 45 M1A1”.
“GHD” crossed cannons ordnance mark.
Also “BNP” stamped indicating its possible use by the British military.
Right side of receiver stamped “Auto Ordnance Corporation, Bridgeport, Connecticut, USA”.
“AOC” stamped on the bottom of the receiver where the front grip mount is fitted.
“US PROPERTY” stamped on the receiver just behind the rear sight.
Left side of receiver also stamped with the ‘Star of David’ Israeli acceptance markings indicating use by the IDF.
Complete with a 30 round magazine marked “The Seymour Products Company, Seymour, Conn.”

 

I read a book on the entire history of the Thompson...however, that was last May, and there were so many details....it is very interesting how these inventers invent these 'perfect' 'tools'......my gandpa had a Thompson...wish I knew where it was at....