For the kind of service you describe, the restoration is typically digital. The provided answer indicates they use Adobe Photoshop (and related graphic tools), with trained retouchers repairing scans of the damaged print.

In practice, the usual workflow is: scan the original photo at high quality, then digitally correct stains, fading, tears, discoloration, and missing areas using retouching tools. There’s no evidence here of special capture methods like infrared or UV, and no indication of chemical restoration being part of the process.

So for water- and mold-damaged paper photos, the restoration shown is most likely a careful high-resolution scan plus skilled Photoshop work—not a special photographic or chemical technique.