Leave them be. They will heal over and be fine.

I would simply cut the stubs off as low as I could with a pair of hand clippers without causing any damage to the trunk.

While flush cuts (removing the branch flush to the trunk or the lower order branch) are inappropriate for trees in the landscape, they are ok for trees that will live out their life in a container, as there is little chance an indoor tree will fail structurally and damage property or people when it fails. There are 2 good ways to approach pruning off dead stubs of trees in containers. First is to cut flush to the trunk. This can be accomplished with a pruning saw, or, there are specialized tools made specifically for pruning flush. These tools, a concave cutter (top) or knob cutter (below) will remove branches and leave a concave depression in the trunk or lower order branch. When callus forms at wound edges and start to cover the wound, it will be least noticeable if a concave cutter was used.

The other method is to allow the short stub to stat on the plant for a year or so. The stub should have any green growth that occurs on it rubbed off, or the stub won't die back to the base. As the rest of the tree continues to grow, you'll see evidence of a branch collar forming around the base of the stub. When you can identify the collar, cut the stub off flush to the distal edge of the collar. This should be used whenever the tree will be planted out, or on trees with thin/smooth bark known to be slow to close wounds. The advantage of leaving the stub until a branch collar forms then cutting flush to the collar lies in the fact it allows the tree to completely compartmentalize the wound to keep any pathogens from spreading to living wood adjacent to the wound. For more on "compartmentalization of decay in trees" and how trees 'wall off' injuries, use the search words CODIT Shigo, or see Wikipedia for CODIT.

Wounds heal faster if you can keep the tissue surrounding the wound moist. When the tissue surrounding the wound dries out, it increases the size of the wound, and callus will need to arise from the wound edges and roll over all the dead parts before the wound closes. I often cover all but small wounds with waterproof wood glue immediately. I 'paint' the wound, being careful not to get glue on the living bark surrounding the wound. Some use Vaseline or even Preperation H to cover wounds so they stay moist. They also make cut paste to cover wound of trees destined to live their lives in pots.

In the center is a large wound on a maple tree due to a trunk chop aimed at increasing a future bonsai tree's taper. You'll see how the wound was covered by callus over time:

This particular wound ^^^ was covered with sphagnum moss (not peat) which was kept moist and covered with aluminum foil. The moss significantly speeds up callus formation.

This is the wound after 1 year. Notice how the wound intentionally comes to a 'V' at the bottom, like an upside down tear drop? That helps make the wound less conspicuous when it's closed.

After 2 years ^^^

After 3 years ^^^

Same tree ^^^ - notice other wounds closing and the taper due to the trunk chop.

Summer 2021 ^^^ - still a young bonsai, but it's 'getting there'.

Al

Thank you all for this information. Thank you Tapla for the photos and how-to, and for taking the time to explain, I appreciate the help. I will look for a concave cutter and clean the stubs up. I do have sphagnum moss on hand to use after the operation. :-)

Glad you found the info useful. Best luck!

Al