[Ernst]

The only motors and actuators permitted on 2012 FRC Robots include:
A. up to 4 CIM motors (part #FR801-001, M4-R0062-12, AM802-001A, or PMR25R-45F-1003),
B. up to 4, in any combination, of the BaneBots motors provided in the KOP (acceptable part numbers are
M7-RS775-12, M7-RS775-18, M5-RS550-12, M5-RS550-12-B, and M3-RS395-12),
C. up to 2 window motors (acceptable part #s are 262100-3030 and 262100-3040),
D. up to 2 FisherPrice motors (acceptable part #s are 00968-2719, 00801-0673, and 00968-9015),
E. up to 2 AndyMark motors (acceptable part # is am-9012),
F. up to 2 AndyMark gearmotors (acceptable part # is am-9014),
G. up to 2 Denso throttle control motors (acceptable part # AE2351000)
H. up to 2 Vex motors (acceptable part # 276-2177)
I. up to 2 window lift, seat, windshield wiper or door motors obtained through either the FIRST-Automotive
Recyclers Association partnership or from a prior years’ KOP.
J. electrical solenoid actuators, no greater than 1 in. stroke and no greater than 10 watts continuous duty,
K. drive motors or fans that are part of a speed controller or COTS computing device
L. an unlimited number of COTS servos with a maximum power rating of 4W each

(emphasis mine)

This is coming from The Robot part of the Manual. If your motor is on the list, then you're good to go.

Also:

[R49]
Motors, servos, and electric solenoids used on the Robot shall not be modified in any way, except as follows:
A. The mounting brackets and/or output shaft/interface may be modified to facilitate the physical connection of
the motor to the Robot and actuated part.
B. The electrical input leads may be trimmed to length as necessary.
C. The locking pins on the window motors (PN 262100-3030 and 262100-3040) may be removed.
D. The connector housings on the window motors (PN 262100-3030 and 262100-3040) may be modified to
facilitate lead connections.

(emphasis mine)

If the motors are allowed, then you are allowed to remove the worm gears.