Carter BBD Question?

I think the cage will pull right out with a hook tool. Just pushed in. You could fill the cavity to see if a leak is happening. If it holds, leave it be.
I have needed to tap the new ball against the cleaned pot metal seat to correct the seat shape. A check ball in Fords 1985 2.8 V6 was a common problem. They would run way too rich. Owners wouldn't bring them in until they flooded out While idling. Screwed up the cat' convertors and oxy sensors. Anyway... They do distort in some carbs. I imagine it could happen in any. Just one tiny spec of foreign material embedded in the pot metal.
Professional rebuild shops have ball end mills to touch/dress with. We do what we can with what we have.