In fact, it wasn't until this morning, while reading the Chicago Tribune's Home & Garden section that I learned what it was and what we need to do. Lucky for me, a responsible homeowner wrote in asking about it.
Now we know that's black knot (Dibotryon morbosum) and that our favorite tree is in fact some sort of plum tree which is commonly affected by this disease. I'm so upset that I didn't act sooner on this, I hope I learn my lesson, but not by destroying our tree first!
Here are some pictures of the tree's limbs with the black knot, you can see that there's a lot of it but it's mainly on the smaller branches.
And the apparent control is this per Michigan State University:
Since the knots are localized, the disease can be controlled by cutting off twigs and branches several inches below the last visible signs of the knot. This should be done during the dormant period (winter).
On large, main branches and trunks, knots should be cut out with a knife or chisel. One inch of healthy bark around the knot should be included in these cuts. Taper the cuts to a point at each end to promote healing.
BURN ALL PRUNINGS OF KNOTTED PARTS BEFORE THE TREES BREAK DORMANCY IN THE SPRING. Spores can develop ad spread from knots left on the ground or in brush piles.
Chemical control procedures are as follows: ½ Tablespoon Benlate plus 1 ½ Tablespoons Captan per gallon of water. Apply the first spray at the early bloom stage (green cluster) and repeat at 7-10 day intervals until mid-June.
However, University of Illinois Hort Center say that fungicides don't help enough to justify the cost. So I guess our first go would be to start cutting down our tree ...
I can't deal with more sickness ... our cat is also sick.