2000 Ford Ranger Hi Pu That Just Had Battery Changed Out By Les Schwab After

HI! I have a 2000 Ford Ranger PU that just had its battery changed out by Les Schwab. After driving it a bit, the 'check engine light' came on. I disconnected the neg. cable for 10 mins to reset. Then I had to take the Ford back to Les Schwab to replace the battery cable terminals. After a couple more days, the CEL came back on. Auto Zone did OBD check and we got a read of P0136. Would installing a new battery short out the O2 Sensor?

Also, after changing out the battery, I found a loose connection right by the battery which I have taken a pic of......can you tell me its importance or where it goes??

Thanks for any help you can give me!! Jodi