Absolutely, if you can manage it, you want to fix this. Almost all off-the-rack mail these days has tube sleeves. To fit correctly, they need to taper from the shoulder to a thinner size at the elbow, and can be a thinner tube for the forearm.
I call it the "wings of mail" problem, because of how they can flap about.
The main reason they don't taper them for you is that everyone has different sized arms, particularly when you take into account different amounts of padding that you might wear with it.
The biggest mistake you can make is to take out too much material. We all do this the first time, if we're not careful. You need to leave enough material to allow the elbow to flex. I
STRONGLY recommend test-fitting by using a lace or butt-links to pinch together a portion of the sleeve where you intend to cut out material, and try it on over whatever foundation garments you use (whether gambeson or just a shirt, or whatever). You'll find that you can't bend your elbows if you try to be too aggressive about it. Remember to do the removal on the underside of the arm, from the armpit to the elbow at a diagonal taper, and then a straight line on the underside of the forearm if the sleeves are that long.
Once you know where you can make your "cuts", you can then go and remove material by undoing the rings as Sir Brian mentioned, and then close the new seam. This is actually easier than making your own mail, in that the pattern is already laid out for you. Even though you'll work on a diagonal, re-adding the links to close the seam is pretty straightforward and doesn't take too long. It'll only be confusing if you haven't worked with mail much.
If you're using riveted mail, I'd recommend erring on the side of taking out too little, rather than too much. You can always adjust again later. I'd still close the seam with butt-links either way, as it'll be hidden on the underside of the arm and will make the work go quickly. Too much room for mistakes with rivets. Or, as Sir Brian mentioned, you can just lace the seam shut.
In the end it makes a huge difference in how the armor fits and moves with you. It'll be more comfortable
and look better too.