In order to use Python in Git Bash for Windows I installed Python 2.7 to C:\Python27 since I had previously only had it installed for ArcMap inside the ArcGIS10.1 folder. I accidentally "overwrote" the files in the Python27 folder but afterwards noticed that all the files are still in the ArcGIS10.1 folder. However after the installation I can no longer access ArcPy from the Python Window inside ArcMap.
This thread seemed to point me in the right direction but my Python folder inside Computer>>HKEY_LOCAL_MACHINE>>SOFTWARE is missing.

I'm wondering if I can simply change a path setting that ArcGIS uses since arcpy and Python27 have not moved to avoid reinstalling anything.