There's no check valve in that vent line. The vent should connect to the inlet side of the pump; I presume so that the pump chamber refills by gravity if the washer reservoir is run completely dry. The tee you're talking about likely connects both pump chambers to the single vent hose. The upper end of the hose is normally nested in the fender wiring harness with the open end tucked under the cross member, high enough so that fluid won't run out of the hose or start to suction.

The check valves are close to the nozzles, one as a tee at the back of the hood and one as an elbow at the right taillight in wagons. The little diaphragms inside eventually degrade, likely hastened by the amount of ethanol in winter washer fluid. Dirt can also be an issue, both there and at the nozzles. Before the advent of easy online ordering, people (like me) used to try fixing these check valves, cracking them open and replacing the little diaphragm inside. They looked like a thicker teflon disk or some kind of other flexible plastic. Some tried using a piece of neoprene glove and some thought the plastic liner inside some toothpaste caps worked mildly well, at least for a short time.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now