Std credit card paid up letter

How long does it take for a person to get a paid up letter and taking my name off itc? I paid off my credit card first week of October and had had to make several trips to the bank just to make a call and ask the same question every single day and each time i call i am told it will take a day or two!!from which day exactly? The reference numbers given dont help much as i am given a different person to deal with each time.

I need answers and a letter asap.