leftover juice from canning pears

Delicious. Add some red wine and make poached pears.

I would add sparkling water to it to make a homemade soda.

Cook it down with more sugar (or brown sugar, or honey) and maybe a couple of those canned pears and use it as a glaze to baste onto chicken or a baked ham. Add some spices to balance out the sweetness; maybe cardamom, coriander, cumin, cloves, etc.

Make a pear cocktail and enter it into this weeks contest!!!

Whenever I have left-over sweetened juices/syrups, I try to use them in either booze (I bet pear syrup would go great in a kir or mixed with vodka) or as a flavoring/sweetener for whipped cream. You could also use it to fill up baked apples (use instead of maple syrup or honey). I think some crunchy granola over apples baked with the syrup would be delicious!

That sounds delicious, not just as iced tea: start instead hot fruit punch & mulled wine season early and add your syrup to those (or just use to sweeten plain black tea to give it a fruity note).
Or you could boil it down to reduce it to a thicker consistency and drizzle over all kinds of things: panna cotta, ice cream, yoghurt… use to soak cake cubes / ladyfingers in a trifle or pear tiramisù.

You could use it to moisten a sponge cake before filling and frosting. It would be delicious in iced tea, but we're sort of out of that season.