I took the gate out on the 101 and plugged it directly into the MOTM-110
CV input
The 110 CV input "wants to see" a CV, not a gate (though the action you describe sounds more like a trigger anyway), it actually should do something if the gate is of any usable level (like 5V) -- it should at least go on and off. You'll want to have some sort of envelope out (probably not available on the SH 101) to use the 110 CV input.
Before you disconnect it however, try turning the gain all the way up on the 110 and see if the 300 is working correctly with the SH 101 CV.
JB