On the surface, I'm not sure that I see anything wrong with their group. I'm against "illegal guns" too - that is, guns obtained illegally or in the hands of people who are not legally eligible to own or possess one.
From their website:
One of the most difficult challenges we face in meeting this responsibility is preventing criminals from illegally obtaining guns and preventing those who do get them from using them. The issue of illegal guns is not conservative or liberal; it is an issue of law and order -- and life or death.
We respect the rights of law abiding citizens to own guns, and we recognize that the vast majority of gun dealers carefully follow the law. Our only interest is in fighting crime -- and we are determined to win. The polarizing rhetoric of gun politics on all sides only obscures the tragic reality we see every day on our streets: violent criminals with easy access to firearms.
They even say "gun politics on all sides", which is interesting by itself. I'm good with what they say above. I dont view them as a threat from what I see so far.
ETA - We still should be watchful though, as Bloomberg has a way of twisting what's right into something wrong.