Don't see them actually eating the seed, but they sure seem to be attracted to them.

Day Geckos love nectar, not seeds - most likely looking for that or insects attracted to the palm.

I believe geckos are insectivores, not vegetarians. I see geckos lapping up ants and flies quite often. When I repot palms or mix my soil sometimes I see little green lizards watching from a distance. When they see something interesting they dart in and snatch it up. I've never seen a gecko chewing on seeds or leaves. If something is attacking your palms I'd look for bonafide pests such as mealybugs, mites or even rabbits or rats.

I love those little day geckos. 

15 minutes ago, PalmatierMeg said:

I believe geckos are insectivores, not vegetarians.

Geckos in a majority of genus,  yes,  majority of their diet consists of insects. 

Day Geckoes ( Genus Phelsuma ) are different.  While they too consume insects,  a sizable portion of their diet consists of nectar, pollen and various soft fruit, ..like Bananas or Papaya. 

They'll even sneak a lick or two of a sweet Mai Tai if they're able to. 

 

This happened while I was cleaning up and/or repotting some of my Dyckias yesterday. I started to go to the garden shed to get a pot. I looked down and saw a 4" gecko scurrying beside me but 3-4' away from my clodhopper shoes. I paused. The gecko paused and I observed his head tilted to the left so he could look up at me. I started to walk and the gecko scurried in lock step with me. I paused again and so did he, head tilted so he could peer into my eye. I grabbed the pot I wanted and when I turned around, he was gone. I didn't see him again but I knew he was close by and watching me work with my plants and dirt. I have a feeling he was eating well, i.e., bugs from what I provided and certainly not Dyckia seeds.

I make it a practice not to harass, try to capture or intentionally cause any of my local geckos problems and he somehow knows this. He was not some mindless automatron just a guy seeking a tasty meal. People underestimate the intelligence of animals. For a lizard this gecko had some brainpower. So do his fellow geckos. If you got them, be glad.

21 hours ago, PalmatierMeg said:

This happened while I was cleaning up and/or repotting some of my Dyckias yesterday. I started to go to the garden shed to get a pot. I looked down and saw a 4" gecko scurrying beside me but 3-4' away from my clodhopper shoes. I paused. The gecko paused and I observed his head tilted to the left so he could look up at me. I started to walk and the gecko scurried in lock step with me. I paused again and so did he, head tilted so he could peer into my eye. I grabbed the pot I wanted and when I turned around, he was gone. I didn't see him again but I knew he was close by and watching me work with my plants and dirt. I have a feeling he was eating well, i.e., bugs from what I provided and certainly not Dyckia seeds.

I make it a practice not to harass, try to capture or intentionally cause any of my local geckos problems and he somehow knows this. He was not some mindless automatron just a guy seeking a tasty meal. People underestimate the intelligence of animals. For a lizard this gecko had some brainpower. So do his fellow geckos. If you got them, be glad.

They poop inside the house here, so I catch them and throw them outside if one gets inside. Never try to hurt them.