I have to wonder what happened to all the original mortar? Where's it all gone?! First of all, repointing would of course be better than what you have there. However, it would be next to impossible to get a decent amount of mortar in there and do a satisfactory job. Some of the bricks look as though they've 'walked' a bit as well. Are these bricks supporting any load or can you pull them out freely?
If the weight of the bay is carried by something else - like like the windowsill or, I see something like a concrete lintel? in the photo, then you could draw the bricks out a few at a time in groups and re-lay them, as they'll have no weight on them. Very tedious though. Getting the mortar in the space at the top of the last brick layer to go back in is tricky too - you typically need to make a stiffish mix and pack it in the gap as you have no space to work of course.
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