Once I finally caught another cricket (let it out on the floor first, dang it), I fed Anansi again. I didn't try to wait it out this time, I put her right back down on my desk. I sat for a while talking and then thought I'd check. I leaned in close trying to see if she had the cricket in her grasp yet. I noticed the cricket a little way in front of her... then she suddenly pounced (as much as a T pounces). It was like she was jumping right at me. I couldn't have timed it better without a lot of patience. lol
I bet the remains are gone again. I swear I need to set up a video camera or something to see what she is doing with them!