3 Answers

I agree with Colleen, you do not have to remove them.

Seed removal is optional. You do not have to remove them. 

How to dehydrate tomatoes

Use tomatoes of uniform size for most even results.

Set the dehydrator temperature at 135º-140ºF. (If your dehydrator doesn’t have a thermostat, set a cooking thermometer in the bottom tray.)
Wash and dry tomatoes.
Remove skins (optional). With a knife, cut an X on the bottom of the tomato, just deep enough to penetrate the skin. Drop tomato into boiling water. Blanch for 20-30 seconds. Use a slotted spoon to remove tomato from boiling water. Immerse tomato in ice water. Use knife to remove tomato core. Skin will slip off.
Core tomatoes (whether skinned or not). Remove tomato ends.
Cut tomatoes.
Roma tomatoes: cut in halves or quarters
Cherry tomatoes: cut in half
Slicing tomatoes: cut into ¼” slices
Seed tomatoes (optional). With a spoon or your finger, scoop seeds from tomato, leaving pulp. Blot extra juice on tomatoes with a paper towel.
Spray dehydrator trays with a very light coating of vegetable spray or rub them with just a touch of olive oil to prevent tomatoes from sticking.
Place tomatoes cut-side up on dehydrator trays, about ½” apart. Do not allow tomatoes to touch. Sprinkle tomatoes with salt, garlic powder, or fresh herbs (as desired).
Allow 1-2” between each dehydrator rack for good air circulation.
Dry tomatoes. Check them regularly. If necessary, rotate racks to allow tomatoes to dry evenly. Remove pieces that dry before others to prevent them from scorching. Average dry time in a dehydrator is 8-12 hours.
Dried tomatoes will be reduced in size, shriveled and leathery, but not tacky. Remove tomatoes from the dehydrator and allow them to cool thoroughly.
Pack tightly in freezer bags, vacuum sealed bags, plastic containers, or jars. http://www.tomatodirt.com/dehydrating-tomatoes.html

Because cherry tomatoes are so small, it seems that removing the seeds would also remove quite a bit of the pulp, leaving little but a chewy rind.   
 

Here's a website for dehydrating cherry tomatoes in 5 easy steps:
info.orschelnfarmhome.com/.../5-Easy-Steps-to-Dehydrate-Cherry-Tomatoes