I have a small pear tree out front, one of those grafted ones that
has 5 different varieties. It just finished blooming, and now it looks
like it has 200 to 250 tiny pears on it, since the petals fell off.

The tree was planted a year ago in early spring, so it has some roots
established. However, last year was very hot and dry, so it was under
some stress, and kind of just sat there. Also, I left on the 3 tiny
pears it had on in the pot at the garden center, so we got to eat 3
pears just a few months after planting it. It is about 5' tall, and the
base is approximately 1.25" across.

Complicating matters is that during the summer, I removed the plastic
tree wrap it had around the base, and discovered that the trunk is
girdled about 1/2 of the way around. I think this damage was caused by
the tree falling during transport, or at the nursery. I believe that
the plant vigor is limited by this, though I am hoping that over time,
especially since the tree is so small at this point, the living portion
of the tree will spread and cover up the dead part, so that the entire
trunk about a foot off the ground will be carrying nutrients up to the rest.

So, my question is this: given that it successfully had 3 pears on it
last year, and has a better root system now, but also considering the
partially girdled trunk, how many of the tiny pears should I leave on
the tree and allow to develop?

Thanks!