How important is it have the resistors on the back of the motors?

Can they be run that way or cause damage to the Clark board?

Stince, the ceramic disc capacitor you see on motors are actually filters to prevent any sparks/electrical noises from interfering with the electronics.

I don't usually pay much attention to it. If it comes with them I will leave them on, otherwise I just do without. I am not too sure if it has something to do with the quality of the motors and also how har drive them.

I've never ADDED them on purpose, it's a bit of a throwback to 72MHZ days of R/C when radio interference was real. 

There is a near zero chance of the lack of capacitors affecting the Clark board functions, it's a radio noise thing.