Young kids often go through like/dislike spells with people close to them, even their own parents and grandparents. They're still figuring out who they are, to themselves, and in relation to other people.
You see your mom as warm and loving, and she almost certainly is. Your son may experience her as overwhelming, possessive, or any number of other impressions, and these would be physical/emotional impressions, not something he'd likely be able to describe. So his reaction may simply be a mystery, until it passes. And these things do eventually pass.
How is your mom with this behavior? If she's cool with hanging back and giving him time to come around, that might be the best you can hope for just now. As your son continues to develop his autonomous "self" over the next few months, his preferences may well change and he'll decide she's the kitten's mittens, and somebody else might look unattractive to him.
You can't talk a child or an adult into liking what they don't like, or loving someone they don't love. You probably can't do it yourself. It's simply not a mental process, or at least not until we become very advanced in our cognitive and spiritual lives.
But you could instruct your son patiently in how to greet people, including his gran. There could be an agreed verbal message ("Hello, pleased to meet you/see you.") and perhaps a handshake. She'd have to be on board with that, too, though.