How you give capsules to a goose is by applying pressure to the corner of the mouth with one hand and when she opens her mouth wrap your hand around the top of the bill, this can help prevent her from biting down, then insert the pill as far down her throat as you can reach, then close her mouth and hold her head upright for a moment. The faster you do this the easier it is and less stressful it is for her.
I had one of mine on chelation therapy briefly for suspected lead ingestion, it turned out to be unnecessary as that wasn’t the problem but this is what the vet told me at the time. Lead is very hard to remove from the body, and even when the problem object is removed or dissolved and symptoms seem to be gone, symptoms can re-emerge at a later date, in female geese and swans it usually coincides when they start laying as the lead has settled in their bones and when they start laying they begin using stored calcium in their bones, which causes the lead to start recirculating in the blood stream.
It can take weeks to months of chelation therapy to remove it, and sometimes it can still re-emerge.
Assuming this was the cause of her problems when she was sick before it’s surprising that the washer hasn’t completely dissolved in some ways but it also is a problem as it’s still there so it will likely remain there for many more weeks to months continuing to poison her, it’s crucial that the washer is removed. It’s possible that her previous illness was actually unrelated and that she swallowed the washer more recently, lead poisoning is a severe health issue and usually isn’t gradual unless she’s been exposed to low dosages over a long period of time.
If you can afford it you should have them attempt to remove it again as the poisoning will worsen as her body breaks it down. As it is now I’m sorry to tell you this but her prognosis isn’t good.
If you can try to get her to eat cilantro and if she doesn’t blend it up and feed it to her via tube feeding. Cilantro has some effect at scrubbing metals out of the digestive tract.