Thank you everyone for the feedback.
The logo is an illustrator file with a transparent background.
I tried many things from recoloring the shatter map to making it all black with a transparent background.
Ultimately, I’ve discovered that if I make all the dots black in illustrator and apply the shatter map to that, then apply my colored logo as the texture layer, I get rid of the artifacts and have the logo in the color I want.
Whew… that took a bit of futzing.