I would use masking tape before the engrave. Ali express has replacements.
You could try oil. Or sanding.
Not sure it is safe to laser engrave something like this anyway. There is a chance it contains chlorine that will destroy your machine. I believe they are made from fluoroelastomer rubber.
“Fluoroelastomer , also called fluorocarbon elastomer, any of a number of synthetic rubbers made by copolymerizing various combinations of vinylidene fluoride (CH2=CF2), hexafluoropropylene (CF2=CFCF3), chlorotrifluoroethylene (CF2=CFCl), and tetrafluoroethylene (C2=F4).”
What type of oil?
What you have is soot–you need something that grabs the soot, water alone can’t do it. Try some dish soap (degreaser) with the toothbrush.
If that doesn’t work, use a bit of white vinegar. Then move to more chemicals: rubbing alcohol, if that doesn’t work, move to acetone (nail polish remover containing it if don’t have the tins from a hardware store)… more/stronger chemicals might start affecting the strap material, though.
But not sure if the material lets you remove it now–maybe before trying anything else, first try rubbing tape over it and pulling off (this is the best way to get soot off suede vs. soap & water scrub). But do note what @primal_healer noted–you may not want to do this again with an Apple strap. You can buy the connections and make your own strap with a material that is laser safe!
Moving this over to Beyond the Manual so we don’t cause the Friendly Neighborhood Lawyers to have palpitations… 
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