greenmanFor that matter

The expression for that matter is used to emphasize that the second piece of information is also true and relevant in the same sense. It's like saying "while we are on the subject, this is also true and relevant".

E.g.

My grandpa doesn't like chocolate, or anything sweet for that matter —A mi abuelo no le gusta el chocolate, ni nada dulce en realidad

Hillary is lier. So is her husband, for that matter —Hillary es una mentirosa. Y ya que estamos con este tema, tambíen lo es su marido 

What's wrong with drinking a couple of beers —or a couple of glasses of wine, for that matter? - ¿Qué hay de malo en beberse un par de cervezas —o, si vamos al caso, un par de vinos?

Whatever you think of Trump —or Clinton, for that matter—it has been an entertaining campaign — Independientemente de lo que opines de Trump —o de Clinton, si vamos al caso— ha sido una campaña entretenida.