I feed a few of my leos outside their homes when I need to. Its a great idea in certain situations:
This helps less-agile hunters and encourages the leos to eat more to fatten them up. Its also the best solution for feeding some colonies/groups/babies. If you throw the prey in their cage/bin, the leos at the bottom of the pecking order may not get equal amounts of food, or even any food. Separate feeding times and tanks solve the problem. Plus, you know exactly how much they are eating.
Also, this saves you from spending time removing the loose crickets by hand after feeding. This way, you just dump the bugs left in the plastic cage/critter keeper back into the box/tub/tank you keep & gut load your crickets in.
It takes the leos one or 2 times to get used to feeding outside their homes -- Do this at night when its dark -- I put the leo in the feeding tank, throw in some crickets or other moving prey items, place the tank in a quiet area of the room, turn off the lights, and leave them for 15-30 minutes.
A sick baby I got from my vet office would not eat at all. After months of slurry force feeding and medicating, I started leaving him in his food tank with some crickets at the same time every night. Initally he was scared of the crickets and wanted out. On night 3, he started eating on his own. I would leave him in there for as long as it took. Eventually he'd eat everything.
A Word on Removing Cage Furniture:
I personally think its a terrible idea to remove cage furniture and hides from the leos' homes before feeding insects. This should be the leos' "safe place" and I prefer not to remove anything unless I'm cleaning (and in this situation, I'd have already moved the geckos fist). I will spot clean and remove humid hides to rewet them when the leos aren't in them, but otherwise I would avoid unsettling them by removing anything. Just think how stressed out they get when you clean and/or rearrange the set-up...
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Too many Leos
1.0 feline "Spot"
0.1 canine "Tika"