I would start by removing the rear wheels and cleaning and greasing the wheel clutches. You will need a small pair of ring pliers. Remove the clip, collar washer, and gear. When Watch which way the gears come off so you get them back on properly the first time. When the gear is removed, there is a 1/2 moon key that will drop out and a small spring in the slot. Have fun.

An HRB216TDA still running? Wow. I had one which was a pretty good mower but sold it because the cutting height only went to 3". I was only using it in the spring and fall, using a Lawn-Boy 10550 in the summer when I needed 3.5". I eventually got rid of that one too and now have two boringly dependable LB 4-cycle mowers that can cut up to 4". I sold that Honda to a guy starting a lawn care business. Come to think of it, mine was starting to drag on the pull-back too. The 3-speed shifter was poor, not having a good detent at each speed setting. I eventually gave up and just left it in 2. 3 was good for finishing up with a thunderstorm coming - it was almost a run - definitely a fast walk. Other than that, it leaked oil constantly when running around the governor shaft - enough so that the wood floor in my shed still has a big oil stain from it. Well, it also has another one from where the LB 10550 float stuck and drained the gas tank after I parked it. Most Honda OHC engines leak around the governor shaft but it's just a nuisance that you wash off twice a year.
Look underneath the mower and inside the belt tunnel to make sure all old clippings are cleaned from the drive mechanisms. You might also let some light lube drip down into the cable housing and lube the wire bail ends.

Cleaning and lubing the ratchets/clutches will fix the pull-back as already posted.

It never hurts to lubricate the rear wheels and paws. I do not think this is your problem.
The paws engage when the transmission is turning. The paws will also engage when you pull the lawnmower backwards.
I would suggest to check your drive cable or see if the transmission belt area is dirty.
So, when you pull your mower backwards the wheels are turning the axle and transmission. If your belt is bound in any way you are trying to turn the engine.
BTW this is a common problem on the HRB216 TDA and Hxa.

Ah, yes rosemallow is correct! Grass in the pulley's are something to watch over as well.

PAWLS

othersise known as 'ratchets'.

I've had my mower for about ten years now, it was used when I got it,It has never failed to start on first pull, even when it had sit over the winter.I 'v taken fairly good care of it,just dont know why I had to put TOO transmissions in,wheels I can understand, but not TOO new $90.00 transmissions.I love the mower it is very dependable,why does a 12 year old transmission cost so much.

Too huh?

only $90?

must be 2011 price