This is a very important question.
Debt SETTLEMENT companies tell you to stop paying your creditor and pay them instead. Then after a while(months to years later) when you have enough money with them they "negotiate" with the creditor. The problem is that during this time you are not paying the creditor so you are in default. There is also no law that says a company has to negotiate, in fact more and more are refusing to.
A true Debt MANAGEMENT companies still have you pay them. However, instead of putting the money into an account they pay the creditors an agreed upon amount each month. This not only reduces your debt, but it also brings you into "current" status.
Now, if you are with a Debt Settlement company, since you are in default with the credit card they can sue you. Often once they find out you are with a settlement company they WILL sue you. So if this is your case and you have multiple credit cards, expect the Target card to be the first, but definitely not the last. In court you really have no defense because you voluntarily stopped paying them in trying to get a better "deal".
Now, if this is a Debt Management Company when you go to court bring all of your paperwork with you. This includes information from the Debt Management Company showing they made agreements with other credit cards and Target refused. It would help if you can show proof that you are abiding by those agreements. Also, bring proof of your bills and any income you have. This won't get you out of the suit. But the judge could force Target to accept the Debt Management company offer as a term of the judgment.
But what ever you do and regardless if you are with a Settlement or Management company, you MUST go to court. If not they will automatically get a default judgment against you.