Mirror modifier active after applying Blender Version 
2.79b (2.79b 2018-03-22, Blender Foundation)

Issue:
As per the screenshot the mirror modifier still appears to be active (see the crease I added) even though it is no longer seen under the "modifiers" section of this object.

I'm quite new to Blender.  Is this a bug or something I am doing?
You are in the Sculpt mode. Turn off Symmetry/Lock in the T-panel