6 yr old medical collections

[syrch]

I have a collections on my account that is 6 years old. Its for $390 and i want to clear this up. I talked to them on the phone and no matter what i say i can not get them to budget out a settlement nor did they say they would remove this from my credit report once paid. Where should i go from here. I have them sending me a letter telling me exactly what is owed. Do i respond to that letter saying that I will pay the amount as long as they mark it for full deletion? I want to buy a house in a year and really want this off my record. Please any help is greatly appreciated. I am clearly a rookie at this and need a little guidance.

 

On a side note the balance is legit. It is a copay that my mother was responsible for while i was in college.