To be "after the money" means to do something with the top priority being to make money from it. For example, some people want to be doctors because they are "after the money," not because they want to help others. In your example, money is NOT the top priority because they are "not after the money."

"We aren't [going] after your money" means "We aren't trying to get the money." Another way to say it would be "We aren't in it for the money." If a woman is marrying a man just because he's rich, people would say "she's only after his money" or "she's only in it for his money". If a child is giving his mother lots of compliments, she might ask him, "why are you trying to flatter me, what are you after?"