i have a 2003 tls and i just noticed that sometimes when i hit the gas gently and let go after for a second i hear clicking noises. what is that?

is this familiar to anyone?

 

anyone?

 

This may sound weird, but I had a similar problem that I only heard accelerating or going over a speed bump and it was a clicking like rattle from under the car somewhere that was deceptive...
My service tech knew what it was right away:
The baffle inside one of the mufflers broke loose and was knocking around the inside. He could explain why you couldn't hear it on braking...I couldn't even localize to front or rear of the car, just I knew it was underneath. You couldn't hear it by kicking the muffler either. He hit it from underneath with a rubber mallet slightly, and it reproduced the sound instantly...They replaced the muffler under warranty...
Dunno if this helps, but...