Machine makes a fairly loud squeeling noise for about a minute when water begins to recirculate at beginning of cycle

I found that my squeal was coming from the little rubber boot that seals the pump from the impeller.

I silenced the squeal as follows...

Give it a try. It might work for you, too. It takes about 30 minutes.

1. Unplug the washer.
2. Pull it away from the wall a foot or two.
3. Tip the washer back toward the wall.
4. Have a strong, reliable helper hold the washer in that position -- firmly against the wall.
5. Get down on the floor. Lie on your back and put your head and arm under the washer (that's why you need a good helper!).
6. Unplug the electrical wiring to the pump. (The GWL11 has 2 wiring connectors.)
7. Slide a shallow plastic dishpan under the pump to catch any water.
8. Find and bend back slightly (don't break it!) the plastic retaining latch that holds the pump in place.
9. Rotate the pump counter-clockwise about 60 degrees, until it comes free.
10. Note the angle/position of the pump as you pull it free. This is the same angle/position you'll need when you put it back in, of course.
11. Get out from under the washer -- with the pump, of course.
12. Have your helper lower the washer to the floor.
13. Have your helper clean up any excess water that runs onto the floor.
14. Put the pump on a well-lit table or other surface covered with newspaper.
15. Using a straight blade screwdriver, pry directly underneath the plastic fan (right up against the shaft) to carefully and slowly work it off. Don't lose the small plastic fan bushing!! - which is actually what you are prying against. Also, as you remove the fan and bushing from the shaft, note carefully how the bushing fits on the shaft. There is a right way and a wrong way to put it back!
16. Now, you are ready to remove the motor/shaft/impeller assembly from the bearings/windings assembly. But first!! Find on the white plastic impeller frame the locking tab that was engaged with the latch in step 8 above - and put a piece of tape on the black bearing/windings assembly to mark the tab's position for reassembly.
17. Using a 7mm socket (or end) wrench, remove the 2 bolts holding the impeller/shaft assembly to the bearings/windings assembly.
18. Carefully pull the impeller/shaft assembly from the bearings/windings.
19. Spray the bearings with a high-quality silicone lubricant. Buy a small can. It is worth it. Do not use WD-40 or 3-in-1 Oil!
20. Using toothpicks, Q-tips, and paper towels, clean any dust, dirt, and hair from the bearings.
21. Spray the impeller shaft and rubber boot inside the white plastic framework with silicone lubricant.
22. Using toothpicks and bits of paper towel, clean the shaft around the boot. Move the shaft back and forth a few millimeters to compact the dusty, hairy crud - so you can spear it with a toothpick and pull it away. Using a toothpick, stuff a shred of paper towel inside the white plastic framework and rotate the shaft. Remove the dirty paper towel shred. Spray more silicone onto shaft and boot. Repeat this cleaning process until paper towel comes out clean. It is a little like building a ship in a bottle - but quite doable.
23. Once everything is clean as a whistle, put a spritz of silicone lubricant in each sleeve bearing and on the impeller shaft near the rubber boot.
24. Re-assemble everything in the reverse order starting with step 18 above.
25. Test out your fix with your helper and...
26. If no squeal, bask in the glow of gratitude and self-confidence!
27. If it still squeals, order a new pump.

BTW - Cleaning all dust out from under the washer a couple times a year should help prevent pump squealing in the future.