Thank you for the background. That's quite interesting because it puts everything in context. The rugs have a history.
While the photos are of good resolution, they are not of the detail we need to perhaps say one way or the other regarding material content. As you may have seen in other areas of the forum, there are serious limitations to estimating the actual material content. If you suspect there may be silk, there are methods of extracting a knot and testing. In briefly looking at the images provided, the rug appears to be quite old, perhaps 1880. It's not improbable it could be older, but we have to be relatively conservative. The red may be of another material than wool, however, common to Agra made carpets are cotton pile rugs, which can feel similar to silk. It is also possible the wool is quite fine and feels like silk. Most probably, the difference felt is due to the recess of what appears to me to possibly be wool. The red dye perhaps had a mordant or other acidic element that has eaten away at the wool at a different rate than the adjacent greens, golds, beige, etc. So this would explain some of the recess. Some stronger deterioration in some areas over other may be a combination of UV exposure with patterned wear, or perhaps other.