Is that pulley making any noise?
Is that pulley seized?
Are you going to replace the pulley?
If the answer is no all of those questions then, there is no need to take it off.
If you are replacing it, spray some penetrating oil around the mounting stud and let it soak for a while. A puller or two pry bars under the pulley will work. If you are replacing, it won’t matter if you mess up the old pulley. Just don’t booger up the mounting stud or bracket. Before putting on a new pulley, lightly sand the stud, where the bearing sits and apply a light film of oil, grease, or anti seize. Mount the new pulley and carry on.