Remove the bad LED from the plug so you can re-use the plug. Notice the new LED has one leg longer than the other.

The long lead goes into the side of the plug with the key as shown in the picture.

The bulb of the LED may not seat perfectly but who cares, it will be under the plastic faceted bulb cover.

Bend the leads up and cut.

Try bulb in your "good" strand if you have one. If it works, put it into your bad strand and see if that has fixed the problem. If not, you know the LED is good now, so go on to the next one.