I'd lay money on those LEDs being the source of your click (I can't say why when you've breadboarded it, that the click disappeared - you schematic photo/scan isn't complete).
When the PIC switches on those LEDS, there's a small transient of current running which get's into the PIC VCC rail, this in turn gets into the TL072 supply, which in turn gets into your signal....becuase a guitar signal is so small, this current jolt is right there in with it & gets amplified up big time.
The solution is normally to have a separate regulated rail for your digital & your analogue (and the ground planes come to that) ...or you could disconnect the LEDs!