Ah! My mistake!
I thought the M1897 trench gun also took the M1905 bayonet (which would be in the M1910 scabbard).
The M1917 bayonet modeled on the British Pattern 1913 bayonet (to fit on the US manufactured M1917 rifle) did indeed have a green leather covered scabbard and was the bayonet issued for the M1897 trench gun, as well.
Thanks! Learned something new today!