I have a 4 year old granddaughter, and she has a very bad habbit of throwing a tantrum.What should I do?

The same thing you did when your kids had tantrums -- Ignore it and walk away -- when the tantrum is over explain to her that Grandma doesn't like that behaviour and if she wants to play with Grandma she needs to act nicely. Alternatively you can pretend it never happened and don't refer to it at all and continue with what you were doing once the tantrum is over.