Charlieplexing: a LED producing light very slightly, although it shoudln't, based on its forward voltage
For some reason, red LED's are faintly visible even with very small currents flowing through them. In the past, I have had this problem before, and used a parallel resistor to suppress it. Basically, you put  a resistor in parallel with the LED. This gives the current an alternate pathway, and lowers the forward voltage to the point that the LED does not glow.

For you this translates to putting a resistor from A to B. This may not work, because adding a resistor from A to B could create other problems. But it is worth a try. You may need to fine-tune the resistor value. If the resistor is too small, it may cause green LED 5 to turn on. And if it is too large, it may not solve the problem. And depending on what other configurations you have (with A, B and C) it could cause other problems.

If possible, I suggest you measure the current, and use that to help pick a starting resistor value. If that is too difficult, just experiment with a range. Maybe try 100k to start, and work downward if that does not do the trick. If this is a production design, you should explore the effects of temperature before you finalize the design. If you are only making one or two, then it is less critical to determine full working envelope.

Good luck!