Thank you very much. I will introduce myself better during the day. I will also post pictures of what I have. Thank you.Splash is when a chicken has two copies of the blue gene. For a chicken that is otherwise black, if it chicken has two blue genes is is splash; if it has one blue gene it is blue; and if it has no blue genes it looks black.
For a chicken that would otherwise be chocolate, one blue gene would turn it mauve, and two blue genes would make it even lighter in color (I don't know the name for the color caused by splash + chocolate).
So if your chickens look chocolate (not mauve), they should not have any blue genes. That means you are just dealing with chocolate chickens and a bit of white leakage.
If you hatch chicks from your current rooster and hens, I would expect all the chicks to be chocolate. Probably some will have the white markings but some may not.
I think the main way to correct this fault is to hatch a large number of chicks, and choose the ones with the least white (preferably no white at all).
You could post photos of your chickens, and we'll see if the white markings have any sort of pattern that someone might recognize. If there is a particular gene involved, there might be specific breeding strategies that can save a bit of time & effort.
Just a note, it usually works better to post a new thread with your question, instead of adding it to an older thread that was started by someone else. It is pretty common to have a question that sounds "the same" as a different one, but actually has a different answer because there is a not-obvious difference.
[Edited to fix the last paragraph, because it accidentally posted before I was done.]