If I take the sim card out would the owner be able to track the iphone?

Okay so I found this iPhone 4/4s and I gave it to the people in the mall they gave it back to me because the owner didn't claim it in 2 months. The phone still has service and it's working correctly. What would happen if the owner started to track the iPhone and traced it back to me. Is there a way for them to trace it back to me? Even tho I took out the sim card?

They can track the IMEI NUMBER on the phone so it doesn't matter if you take the simcard out