"These are individual rings that look grooved right into the top of the receiver."
Only if the "1981 BDL" is a rim fire. So first tell us what a 1981 BDL actually is.
In my opinion, the Kwiksite see thru rings are a joke. I'm not sure if the company made a direct mount(vs separate bases & rings)non-see thru set up. If these are of that type and they've held zero for previous use, I see no reason to change. The only advantage of having separate bases & rings is the convenience of being able to remove the scope w/o completely dismantling the set-up.
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