Why: They should be removed because it’s almost impossible to miss a target at that range. It has been debated that Han shooting first shows an unprovoked attack on an individual, but it’s clear that Greedo was going to shoot him and that it was mostly in self defense.
How: Remove the shots and restore the original footage. It would also be cool to see how Greedo gets fried more clearly, like showing an orange beam covering his body, like the vaporizing effect from "Jedi Outcast", then showing some smoke coming off his charred body before he drops on the table. This could all be done with CGI.