You might want to dilute it by adding a lot of other materials to it. If all you are adding is kitchen scraps, you need some browns anyway. Without browns the kitchen scraps may get smelly from too much nitrogen. The high pH will exacerbate this by driving off ammonia. Mix in dry leaves or other vegetation, shredded paper, sawdust or wood chips. Eventually it should balance out.

If you have a lawn, and your soil isn't alkaline already, you can spread a lot of ashes on a lawn and still have a very thin layer. Just sayin'.

No harm done and I agree, just add more brown and green materials, mix and water in and you should be fine.

Whether those ashes will have an adverse affect on your compost will depend on the ratio of that ash to everything else. Wood Ash is very alkaline and that can cause the bacteria to move, or it could kill them off if too much is added in one place, ie. the ash is not well mixed in the pile.
Adding more material will change the ratio of ash to everything else and turning the material can, maybe, make the ash more evenly distributed.