Those are called burr knots. The tree is trying to form roots. Around here they aren't a problem that I've seen. But they can be a place where borers attack. It's sometimes recommended to let them root by mounding soil. But those look pretty high on the tree and if you let the scion root you may get a very big tree.

Thank you fruitnut! They are about a foot and a half about ground level -- I am not sure I can mound soil around them unless I create a special raised bed for them. By "letting the scion root" are you suggesting I cut the branch below the burr knot and plant it in soil?

You can't do anything that high up. Just watch for borer. You'll probably not have any serious issues.

Thanks, fruitnut. Fingers crossed.

He means that if the tree is trying to grow additional roots, its usually because it thinks it needs it. If this was happening below the graft union it would be good to hill up and let the tree have it's way.

However, being that far above the graft union you're looking at the scion trying to put down it's own roots instead of using the grafted rootstock it has now. Most of the time apple trees are on dwarfing rootstock as those trees can get HUGE on their own. As in 40+ feet huge.

If you let that scion root, it would start growing like a normal apple tree again, meaning it would grow very large very quickly (as well as possible added problems with soil pests and diseases).

So yeah, the scion is likely trying to grow bigger faster than the dwarfing rootstock will let it, so its trying to bypass the rootstock altogether with it's own roots. Long as you don't let it do so, nothing should happen. If it does, well lets hope you have lots of space...