I think DadiOH has it right. The OP said there is a gap between the
sink and the backsplash, not between the sink and the cutout. The pic
appears to be a combination of rust and crud. If the sink and counter
were "recently replaced" the OP was either scammed or chose inferior
product. There shouldn't be any caulk between the sink and backsplash--
just keep clean with a small brush and cleanser. The caulk should be
under the rim of the sink.