CEMENT is the same bonding agent used in concrete and mortar. Concrete has rocks and sand in it. Mortar has sand but not rocks because it must squeeze into tight spaces. The new joint is not filled with concrete, but with new, uncolored mortar. You will never be able to match the existing mortar because it's covered with dark colored dirt and mildew. If you matched the dark color, then when the walk was eventually cleaned or pressure washed, you'd have the same spot being dark while the rest of the walk had light mortar. It would be a losing battle. If this problem was mine, I'd get some muriatic acid and CAREFULLY clean only the smeared mortar off of the brick. I think this would best be done with a cheap plastic bristle paint brush used to daub acid in the proper spot, since it's such a small area. (If one has never worked with acid before, a person would need a water hose standing nearby ... acid can work fast and sometimes needs to be flushed away in a hurry. Also, one would need to be upwind of it as the fumes are extremely noxious. And, of course, not splash any on one's skin!) I would not use acid to clean any of the mortar that should be there. Acid is too powerful and will eat into it. After the smeared mortar is cleaned away, I'd pressure wash the walk. This will bring the dark stained color to a much lighter uniform state (the brick will look better, too,) making the new mortar not such an obvious difference. Within a relatively short period of time, the natural aging process would obscure the difference even more ... probably to the point that no one would notice it. Regardless of what you decide to do, you should not try to match dirty mortar. In the long run you would be dissatisfied.

It may be cheaper to replace the entire deck than to level and recoat it. Typically aggregate finishes need to be ground down.

Thanks for your advice! The concrete was actually my idea (haha). The contractor suggested putting flashing around the foundation and then adding soil to grade away from foundation. I asked about the concrete because it seemed like a more permanent and waterproof solution. He's coming back today for a second look to finalize plans and I will ask him about just doing the flashing/grading and possibly a drain around the back perimeter (which sounds like a good idea, anyway). I feel we have to remove the deck and fill in that room because it's so horribly constructed (a deck constructed on top of an open hole in our basement, with just foam insulation separating our house from everything outside? insane! there's no door between our house and the basement, btw). The deck is also rotting from being exposed to so much rain and never being cared for, so it's an eyesore anyway. We've had two other companies come out-- there aren't many options around here. One were total shysters who just wanted to put plastic sheeting on the inside of our BRICK foundation and force the water to run behind it into an interior drain (while growing mold and ruining the foundation)---SO stupid, and for almost the same amount of money as actually fixing the problem. The other could only do a vapor barrier in the crawlspace and install a drain outside. The one we're working with now can do anything we need and is the only company like it around here. Switching to flashing/grading on the sides sounds great (while keeping the concrete patio)-- I'll ask him about that today. It would be really nice if we can get the cost to $5,000.

In my location we pay top dollar. A stained concrete slab with 6" of new concrete would be closer to $ 10/sf. And would take 4-6months to complete. Your project cost $3.25/sf. How long did it take start to finish? It takes 1 day to cure 1mm of poured concrete. One inch = 25.4mm. It works out to be 1 month to cure 1 inch of concrete. You poured 6" of concrete. If they added curing agents to speed things up, the chemicals float to the top and contaminate the surface. The floor contractor HAD to clean that up...extensively! If the skipped that step then the finish would not 'take' the way it was supposed to...as in the stain won't look right NOR will it stick properly. It might look like parts of the floor didn't receive any stain.