Certified GKH Gardening Expert
Since this is a tree that you get fruit from, I would certainly take the sucker down as it is drawing energy from the parent tree, which will affect its fruit production, but it should not cause harm beyond that. If you remove the sucker, be sure to use sharp, clean pruners so as to reduce the chances of disease getting in the wound. You can also dig up the suckers (the term commonly used for these shoots) and pot them up in potting soil. When you dig them, up, make sure some of the roots come with the sucker. Keep them well watered and in the shade. When you see new leaf growth, they are ready to be transplanted into the ground. This process will not hurt the mother plant, but I will warn you that the suckers will not likely look like the mother and may not produce fruit.