My experience with field back-flushing has been that some fraction of flow can be restored, but it takes a more thorough session back home to approach like-new flow. This includes Sawyer and MSR filters using the hollow fiber media.

I've never taken the syringe, instead using a water bag and hose to force water backwards through the cartridge. The bag and spout need to be strong and watertight in order to generate enough pressure.

My worst luck has been source water from brushy shorelines that does not circulate. Clear or cloudy isn't a reliable indicator. (I don't currently hike where glacial silt is present.)

Lately I've been toting a ginormous 10L dirty water bag and especially for 2+ person camps it's terrifically convenient.
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--Rick