Yes, that sounds like the rubber strip that sits on the left side of the hard drive inside the chamber. It has a groove along one side, right? That's the channel down which the bolts on the side of the drive slide. That rubber strip started to come up when I was replacing my drive, too. I pressed it back down into place and slid the drive home as gently as possible to keep the rubber strip from shifting too much.
I'm pretty sure the main purpose of the rubber strip is to protect the drive from getting banged around. It might also prevent its metal parts from touching other metal parts inside the machine. I'd recommend trying to put it back into its place if you can. You should be able to figure out which way it goes by gauging where the channel needs to lie for the bolts on the side of the hard drive to pass down it. If I remember correctly, the channel isn't exactly centered one the strip, and when it's positioned correctly, the edge the channel's closest to is on the top. (That would be the top of the area you're working on, which means the bottom of the laptop, since you've flipped it over to get access to the hard drive.)
You might be able to get it to stay in place just by pressing it down, using something like a chopstick to press it down further in the chamber. Or you might need some kind of adhesive. I'm not sure what kind of adhesive is recommended -- my first thought is a bit of rubber cement, but that might be totally wrong. Maybe some other posters can make more educated suggestions.
NOTE: One big suggestion -- be sure to take note of which way the drive is positioned when you're taking it out of the machine. It's easy to forget and reinsert it the wrong way up, which was how I managed to push my rubber strip loose the first time, since the bolts on the side of the hard drive will then be positioned incorrectly and will drag at the edge of the channel and pull up the strip.