Karen, suckering on ornamental flowering Pear is a common problem that we have on the nursery as well. We have been working on training our Tree pruners to be a little less professional when suckering by tearing away the suckers rather than pruning away.
Unfortunately there is no simple way to overcome this.But I can tell you from my own experience in my landscape that if you keep this a regular priority you will overcome the issue with time. As the Trees mature less of this should be taking place. On a regular basis I would walk my Pears and simply scrape the suckers when young with my boot and I eventually won!
I would seek to damage the suckers with every contact. I remember the frustration with this at times but today the suckering has subsided. Hang in there, you will overcome.