They know you have reduced the cover because you told them, they know you have the same insurance document showing you're covered because the insurance company didn't request it's return, the only way they know you have restored the cover is for the insurance company to inform them, the insurance companies seem to be withholding this information or the NTA are too lazy to ask them, therefore they require you to prove it.
Many here said the lapsing the licence, returning the discs and then undoing same would be simple, that unfortunately doesn't seem to be the case.