The bumper bar / bracket looks to be extruded aluminum.

Pic 4 shows the bracket to be riveted on so it will be somewhat of an ordeal to remove.

Look on the back of the bracket, are the studs single or paired to a strap? If single they are likely serrated ( like a press in wheel stud ) , in that case you can pound the stud out and possibly use one from the old bumper. If there isn't enough room to squeeze the new one in, you might be able to shorten it a bit. If the studs are paired up, you will need to cut the strap first or possibly extract the pair.

Another possibility ,if you don't have enough room for wrench, is to use a bolt from the car end and weld a strap to a nut on the bumper side. The strap on the nut will act as a permanent wrench.