B737 Captain reported the lithium-ion battery on board was incorrectly processed on the forms given by Ramp.

Narrative

Form was given to us by Ramp and we were told that lithium-ion battery on board. The lithium-ion box was checked off with nothing else under subsection A or B checked off. I inquired about the subsections and A was checked off and B was X'd out. I told him that it can't be A and because he said the battery was removed. He was asking around to get additional information because he didn't know what I was talking about with the requirement to verify the subsections. Ultimately; it was confirmed that all of B was now complied with and explained to him that this is what needs to be done and not just check the main lithium-ion box. I was professional about it all and so were they.This happened once before to me in ZZZ1 back in a few years ago but I thought this was an isolated incident and didn't file a report then. The difference with ZZZ1 was that Maintenance had to come on and secure the battery terminals because the passenger had it loose in his carry on instead of a protective case like in the ZZZ incident. In closing; since I was looked at with a blank stare by the Ramp and agents when I explained the procedure at two different stations; I believe now that this might be more systemic than I originally thought. I have experience with lithium-ion fires and it is not pretty and this is why I take this seriously. Thank you for your time.