the answer to that denedps on your current credit score and the factors affecting it. you need to meet with a reputable mortgage loan officer, have your credit run and go over your finances (income and assets) with them. if, with the scores the way they are, you qualify for a new mortgage while carrying the debt then the choice is yours. if not, the loan officer should run a program called a credit analyzer which will tell you what debt to pay down and how much to pay and approximately what difference you can expect in you credit score. the goal of raising your score is to have you qualify for ALL future credit (your new mortgage, future credit cards, car loans and leases etc) at the lowest rate possible.keep in mind, many lenders are now eliminating no down payment and small down payment programs and many of the ones that are left require higher credit scores so the meeting with the loan officer and determining how best to use your money is a must. sometimes even a slightly larger down payment can make a big different in your rate / payment.
They talk to the answering machine, even though it is on 'answer only' mode. They call themselves "credit card services", & say that there is no problem with the credit card, but that you are eligible for a lower interest rate. If it is a legitimate caller, they should identify the card with the expiration date or the last 4 or 5 digits. Otherwise, So far as I am concerned, they are just another solicitor crossing that line of illegality to harrass people via phones registered on the do not call registry.