I'm getting ready to send a PFD to Unique National Collections for $134 I owe my local library. Their verification letter says payment can be made directly to the library. Should I continue by sending a PFD offer to the CA or just go down to the library and pay it then ask the CA to delete it through a GW letter?

The original delinquency is from June 2008.

If the CA says I can pay the library, does that mean the library is still the owner of the account? Should I try asking them to direct their collection agency to remove it from my account?

Thank you in advance for any advice you can give me!