Gheckos are harmless and are beneficial in controlling flying insects such as mosquitoes (as you quite rightly stated).
For reference (Google)
The only thing I have found that not only kills geckos, but really turns them off, and gets them to move on is insect spray. I have had huge geckos in my home before. They are hard to catch. I sprayed them directly on the face with an ample amount of insect spray, and it seemed to really dull them and slow them down.