In my water bed, the bed sheet tends to get pulled off from the corners of movements in the bed. The idea was to fasten them to the corners somehow to prevent this from happening. Fortunately, there are some round holes in the base plate designed to route the bed heating cables through. As such I designed some round clamps attaching the bad sheet to the base plate at those holes, leaving enough space in the hole to route the heating cables through.
I printed the parts with PETG, 0.2mm layer height, and 20% infill. For added strength, I increased the perimeter lines to 3. The parts all print without support. The screw in the current STL files has a diameter tolerance of only 0.2mm, meaning that if your printer is not particularly precise you might need to scale the screw down slightly in X and Y but not Z axis.
Update: I added a V2 with the following changes compared to the initial version: