What is the easiest way to remove chicken leg/drumstick tendons?
Based on your comments, the likely issue is with the pliers you're using.  I doubt that the relatively small set included in a multi-function knife is going to have enough grip to hang on to a slippery tendon.

I'd try a pair of (very, very clean) needle-nose pliers, like so:



They're readily available and inexpensive, so it's probably worth getting a dedicated set for the kitchen; these are also good for other fine, messy tasks like removing fish bones.  You should be able to get a much more secure grip on the tendons this way.  If they still won't pull out easily, try wriggling them back and forth a little perpendicular to the long axis of the bone.