Hi Krone26,
Welcome to the forums! I'll do newbie welcomings in lady V's absence (jk, no one can replace her)
Anyways,
I too have the Explorer I from Joshua, a rep datejust from Trusty, and a gen Datejust from...Rolex haha.
All three of these watches, especially the two datejusts with Jubilee bands, tend to get crud and dirt in them from normal wear and it's a pain to clean.
My Explorer does not have any "black" on the band but I'd assume since there's no ferous/rust/corrosion (usually that reddish stain) that you're probably ok. A good way to tell (I know from freaking out about my first rep band) is to lightly scratch the material with a fingernail or pocket knife. If it comes off, problem solved, it's just crud. If it doesn't, you may want to take some macro pictures and send them to the dealer you purchased it from.
I'd also invest a few dollars (Euro, yen, w/e) in a soft bristled tooth brush and use it to lightly scrub off some of the grime. There are also Cape Cod Polishing Wipes for polished surfaces/cleaning.
I'm not an expert on straps by any means but I'm just telling you what works for me. I'm sure someone like SD, Carlsbadrolex, Stephanie, etc who collect rollies can offer some great advice.