I came across this situation recently.
Even after I removed the offensive mortar joints, there were remnants of cement smeared onto the bricks in places to still be dealt with.
Once I was able to make the mess disappear, I was left with this result and was ready for the replacement mortar.
In the meanwhile, I had proceeded to figure out the proper mortar mix. The vertical joint on the left is my sample. The one on the right shows the house’s original mortar.
And this is the final result.
Here is the review the client has posted on my Google page, should you be curious to know just how satisfied he was.