It is almost impossible to match the color exactly unless you replace all of the grout. Fortunately grout is typically much cheaper in larger quantities.
A fast, easy way to remove unwanted sanded mortar/grout between tile is to use a circular saw with a ripping blade that is less than half the thickness of the tile spacing
(ripping blades have few teeth and a large gullet for good chip removal - you aren't actually cutting the mortar/grout, but essentially chipping it away - for this reason it is extremely important to wear PPE and protect breakables in the surroundings and needless to say the blade will never cut wood again so use an old or cheap one)
The process is quite simple:
Set your circular saw to the depth of the tile by resting the blade on a flat surface between 2 scrap pieces of tile that are the same thickness as your tile
** (You may need to manually move the retractable guard).
- Then loosen the tilt lock knob and allow the tilting base to adjust.
- When it rests flat on the tile with the blade just touching the surface, tighten the tilt lock knob.
- Cover exposed skin (Safety goggles, face shield, gloves, long sleeve shirt & pants, etc...)
Cover breakables (drape a cloth/plastic over windows, lights, and "nick-nacks")
** The small to medium sized bits of mortar/grout will exit the circular saw at a high velocity. If you can devise a catch that will work with your equipment and space, it will be much safer and save a lot of cleanup time.
Once you have your self, area and tools setup, simply guide the saw blade down the center of the grout-line and let the blade chip away the unwanted mortar/grout. This will cover all but the exterior few inches (due to the guides of the saw and curve of the blade) Finish the rest with hand tools (I've found that a cheap appropriately sized flathead screw driver and a hammer work about 8 times as efficient as a grout saw on sanded grout and mortar)