collection credit card paid in full every month. car home loan

a 2nd year resident who will be going for my citizenship this summer and of course am working on my credit. I am originally canadian and worked in the usvi and had a cell phone through sprint. When i got transferred back to canada and they didn't provide the cell phone service there it was agreed that they would keep my deposit and close my account. Well you can guess what happened they kept my money and did not close my account. So almost 5 years later and now back in the usa upon purchasing a vehicle I learned this was on my account still. I contacted sprint and they assured me that this was no fault of mine that the account hadn't been closed and it even stated this in their notes they even gave me copies of the notes left in their system that states that I owe nothing. So 2 collection agencies later from being sold from one to the other I called them and shared that information with them, they weren't interested and stated I had to pay or it would remain on, i even disputed it through credit inform twice and they stated that it was to still be paid with a balance of $224 I told them my concern of paying this again and it not being removed they told me they would post this as satisfied on my credit if I paid it again and stated that the letter would come at the end of paying it and they couldn't agree to having it removed from my account. I didn't get a good feeling from the conversation and this being my first time going through collections on my credit I am worried, I am uncertain what to do at this point and don't want to pay again if I am going to get screwed. I also have plans on purchasing a house as well now in texas and need to get my score up. I have had my limit on my credit card increased from $300-$2750 in less than 18 months due to paying my full limit off every month. Do you have any ideas to get my score up as high as possible by summer so I can purchase a home. Each report shows anywhere from 568-613 at this point everything has always been paid in full before due is it because i haven't had credit for a full two years yet or is it due to the balance on my car loan.

Please help me with this collections issue as well as increasing my score.
----------------------------
use debt validation and pay
negotiate before you pay if possible
ask for paid as agreed and paid in full


pay off anything past due or owed
30 days late, collections
on my credit report
ask for help
reopen credit past bad credit card collection charge off accounts

after 24 months ask for updated to "past 24 months only"