I presume that manual thinning of the fruit due to the quantity and size of the fruit is impractical. There are a range of chemicals that can be used to prevent or reduce fruit production, but none appear to be a good choice for your situation. A common deflowering agent, Florel, when sprayed on a tree, enters the plant, and is converted into ethylene. Ethylene signals to the tree that it is under stress. If applied while the tree is in bloom, Florel will cause most of the flowers to fall off reducing fruit production. Unfortunately, spraying this chemical on a large tree without drift onto non-target plants is difficult to impossible. There are a bunch of other chemicals used in orchards for thinning fruit that have the same problem and, in the case of Sevin, toxicity to bees. Snipper is an injectable chemical that eliminates the drift problem and has been shown to be effective on ornamental fruit trees, but, so far, it is only labeled for use on sweet gum trees (Liquidambar).
Your best choice is to replace the patch of grass under your tree with a ground cover. There are quite a few options:
Mint (Mentha sp.)
Lady's Mantle (Alchemilla mollis)
Sweet Woodruff (Galium odoratum)
Bugleweed (Ajuga reptans)
Plumbago (Ceratostigma plumbaginoides)
Japanese Spurge (Pachysandra terminalis)
Dwarf Cotoneaster (Cotoneaster dammeri)
Perennial Geranium (Geranium macrorrhizum)
St John's Wort (Hypericum calycinum)
Spotted Deadnettle (Lamium maculatum)
Ground Clematis (Clematis recta)
Dwarf Japanese Spirea (Spiraea japonica 'Alpina')
And many others.
It appears that Snipper is now labeled for a variety of ornamentals: Ash,
Black locust, Black walnut, Cherry Cottonwood, Crabapple, Gingko, Hackberry, Hickory,
Honey locust, Maple, Oak, Olive, Persimmon, Plum, Tree of Heaven, Sweet gum, and Sycamore. Ornamental pear is not on the list though. There is another injectable agent for fruit control called Pinscher, which is broadly labeled for ornamentals. Either of these chemicals would have to be applied every spring by a professional arborist.