I think that is what the piece of metal is called but am not sure. Anyways my question is how important is that tiny washer that goes behind it under the cap? I cleaned a bunch of reels yesterday and for whatever reason when I was done I noticed those washers and tbh don't feel like taking them apart again to get the washer back in. I can't get it in without removing the 2 screws to take off the front hood and I don't want to almost totally strip a reel apart just to get that washer back in.

The better the fit between the pawl and worm gear the longer they'll last. In some reels they are optional depending on the fit. If they were in there I'd replace them at some point but it's likely not catastrophic to fish them as they are.