What I see between them is this:
Perhaps they did have a relationship together (though with Gin, is a deep one even possible? --the guy's a block of sharp ice), or maybe he just hates to see his 'prey' get away. He's a very intelligent person, and thus, I'm sure he gathered plenty of information (even as miniscule as her favorite color) on all of his 'underlings' so he could know their every weakness, their viewpoints/thoughts, and enough to bring them down if necessary. In actuality, I'm sure he doesn't have close bonds with anyone so he won't have to worry about emotions getting in the way of taking one down if necessary (like when he pointed a gun towards Vodka, whom is likely perceived as a friend). It seems to be 'just business' with Gin, and in my opinion, he's only focused on killing Sherry because of his pride or that he has the obsession of getting things done right the first time. It probably peeved him to no end that Sherry got away, marring how he appears to the others -- or maybe himself -- because he failed to 'take care' of her.
TML's theory could very well be true as well -- he could want her back for power reasons, or just want to kill her because he lost that 'power'.
Dunno for sure though, just theories and whatnot.
Also -- RJB -- really? That seems like another one of those 'theories' that couldn't possibly be true. Though those types do seem to be in your specialty. Thinking out of the box--or just not thinking at all ?