Hi Everyone. I'm very sorry if this question has already been answered but I have been digging through old threads for awhile now and can't find an answer to my exact situation.

I recently received an unlocked iPhone from a relative in Asia. It is jailbroken because the Installer app is available and it is SIM unlocked because I can use my T-mobile SIM card. I'm not sure what method was used to SIM unlock but I assume it was with AnySIM. What I want to do is restore the phone because it has a lot of stuff that was installed and sometimes I have issues making calls or get horrible static answering an incoming call. I want to know if I can use the restore method on iTunes and if I do will it relock the phone and prevent me from using my T-mobile SIM? The details on my phone are as follows:

Version: 1.1.1 (3A109a)
Model: MA712LL
IMEI: 01 130********
Modem Firmware 04.01.13_G

Thank you very much in advance for any help anyone can provide.