I have done this 2x on my 416C. All Cat and Ford/New Holland brakes will chatter this way especially if you don't have the right oil. I used to use an "equivalent" oil (Chevron) but I had to also add a friction modifier (same if you use Ford/NH oil, at least back then), as was mentioned in the last post. If you don't the brakes make a lot of noise. If you run Cat TDTO you don't need this additive. Just because the brakes are noisy does not mean that they are worn out. I'm not familiar enough with the older Series II backhoes to know if they incorporate the same brake system as my 416C. I suspect that they are the same. If they are hydraulically activated (as are the ones on the 416C) than you will be losing brake fluid if the brakes are worn out. This is because the piston is traveling so far that it goes beyond the seals and allows the brake fluid to escape into the rear diff. If you are not losing brake fluid than I would not be inclined to think that they are worn out.
If you decide that you must replace the brake linings than you must remove the rear axle from the machine (as the last post stated). When I did it, I did not stand the axle on end. I worked on one side at a time, with the axle on the floor. On end can be done (and is the way explained in the manual, though in a stand and not in the wheel) but will require a hoist, or some other way to lift something very heavy, in your shop. The hardest part (for me) was trying to put the piston back together after replacing the linings. It is difficult to do (at least the first time I did it) without tearing the o-rings. Make sure you stretch them really good before attempting to reassemble the piston. I also recommend having a few spares on hand (I went through six before I got the tip I just gave you). You should also coat them with assembly lube. After you have put one side back together there is only one way to check if you have a good seal in the piston. You must put whatever side you are working on back onto the center diff. section. Do not put all the bolts in. Just snug it up with a couple. Make sure the fill plug (of the center section) is out. Put the little round brake manifold (not sure what else to call it) back on the side you just snugged up (it goes on top of the axle and it should have been removed before you took that axle off of the center section). This is the part that the brake line connects to and there is also a bleed valve on it. You are putting it there to seal off that side. Take air pressure (I used the "blow nozzle",the one with the pointed rubber tip, with the rubber tip forcefully held against the brake oil port) and force it into the brake. If you don't hear air escaping into the center section, than your seals are good. You should hear the brakes "clunk" lightly as they are forced together. If you do hear the air escaping, into the ceneter section, than it's time to do that side over again (this is when the spare o-rings come in handy) because one of the o-rings is cut. I should also mention that I used a floor jack (two actually) to pull the rear axle from the backhoe. Be careful if you do this (a transmission jack would probably be better). After I was done with both sides (the first time) the axle fell off of the jack when I was putting the axle back in. It broke the parking brake rotor (on the input shaft). That cost me a day (waiting for the part to arrive) and $500. Even though that happened I was still way ahead when compared to having Cat do the work. Parts cost about $1300 (if I remember correctly), but Cat said they wanted $3500-$4000 to do that job. The second time I did the job in about nine hours without any problems. It is very helpfull to have the service manual in hand (for me at least). Not to bad for a "backyard" mechanic.