The plastic tubing supplying filtered water to our refrigerator currently runs below a suspended ceiling. I want to reroute it above. How do I disconnect it without damage from either the union or tee, so I can reconnect once moved? The tee is labeled NSF-51 Parker Parflex size 4. The union has no discernible markings. I believe I would rather disconnect the union rather than the tee. I didn't want to just start tugging. I have found similar fittings for sale online, but no instructions for use.
Just to add some visuals to the others' explanations using your photo, you need to (1) push on the collar trying to move it parallel to the tube, and (2) pull the tube.
To reconnect, push the tube into the collar until it stops (should be about 1 inch). Make sure the tube end is square (perpendicular to the tube axis, with no damage); cut a bit of the tube if necessary.
This is polypropylene, but the connectors are very similar to PEX quick-connect fittings. You need to push the protruding collar (the inner tube that the polypropylene is secured into) back inside the connector, and you have to apply the pressure to that collar evenly. You might be able to do that if you're gentle enough with a pair of pliers with the jaws on the wide setting, but you could damage the polypro tubing.
The easiest way to do this is with a small tool or device meant for that purpose. The picture below is an illustration of one type of aid. You snap this over the tubing and press it firmly against the shoulder on the connector, and the tubing should pull out easily enough. These will come in the bag with some connectors, or should should be able to find them in the plumbing section of your local big box store.
This is what I call a "push to connect" fitting. They are put together by pushing the tube into the fitting.
They are released by pushing the small collar into the fitting and then pulling out the tube. Sometimes they are slightly stuck, and may take a little bit more force to pull out the tube, but it should be if if the plastic collar is first pushed into the fitting.
Sometimes the tube is slightly damaged or crushed, in which case you'll need to cut off the last little bit of the tube.