You're correct, it's the check valve. Pretty common problem.
First, shut off city water, turn on your water pump and run FW tank water through it for a minute or two. Then go back to city water.
The check valves often get something in them or get mis-aligned.
If the above doesn't work, you'll need to replace the valve.
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1988 Coleman Sequoia - popup (1987-2009) - outlasted 3 Dodge Grand Caravans!
2012 Roo19 - hybrid (2012-2015)
2016 Mini Lite 2503S - tt (2015 - ???)
2011 Traverse LT, 3.6L, FWD
2009 Silverado 1500 Ext Cab, 5.3L, 4x4, 3.73
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