Bottle Cage Mount on Carbon Bike

As you probably know intuitively, a metal tube has the same properties in all directions (the technical term is that it is isotropic). A carbon tube may not have the same properties in all directions, i.e. it can be engineered anisotropically. This is one of the main selling points of carbon. Carbon frame tubes aren't generally engineered to withstand significant clamping force.

That said, this item looks like a pair of ratcheting straps made of nylon or some other plastic. They probably don't close tightly enough to damage the carbon. They should be fine. The question is how securely they will hold the water bottle.

While we don't make recommendations for specific products, if you were thinking of mounting a bottle on the underside of the downtube, then the Apidura Expedition Downtube Pack fits a bottle in a pouch, and has one thick and durable Hypalon strap to secure to the frame. While Apidura is a premium manufacturer, it's likely that other manufacturers will put out similar designs at lower prices.

Another easy option for water bottle carriage is stem bags, which strap to the handlebar and the stem. You can mount one on each side of the stem. These may be called feed bags as well (Apidura uses this term for their own bag). One potential minor downside is that depending on your physical proportions and your bike geometry, your knee may hit the bag when climbing out of the saddle. One 2015 review of a few feed bags is here. Depending on your cockpit setup, some handlebar bags have space for water bottles at either end of the bag, although I believe this arrangement is more common for long-distance road touring than for gravel or bikepacking. Do note that an overly loaded handlebar bag can alter your bike's handing, whereas feedback I've heard from stem bag users is that they don't really change the handling much. You also can't fit that many items in a stem bag.

There are also clamps to fix cages to the handlebars (remember those pictures from olden days) unless those are carbon as well. Cages may also be attached to the rear of the saddle or to the seat-post.

The frame material is likely too thin and will not resist crushing from clamps.

Whether they will work will depend on the shape of your frame. Many carbon frames are tapered, being wider near the headtube and narrowing as the go back. This will mean the clamps will have a tendency to slide toward the narrow end of the tube. A small wrap of inner tube under the clamp may help some but I think it will still be problematic with the weight of the full bottle. I would recommend either a saddle or seatpost mounted cage similar to a Skekane Elite which can hold three cages.

There are also seat-post mounted bottle cages.

See Profile Design Aqua Rack ii Dual Water Bottle Cage (Black) (Seatpost Mount) for an example:

That one even has places for screw-in CO2 cartridges.