How can I remove noise from an audio recording?

"You definitely need some sort of software to filter out the noise. Some of the other answers here can address that.

If you're still doing the recordings and need to stop the cell phone interference, use ferrite beads near the base of each speaker.

By the way, just in case anyone is curious, these can be used for small desktop speakers, too."

Try out something like Audible for Macs, and Sound Forge or Adobe Audition for Windows. The latter should do it real well. You will likely have to build a custom ex to cut out at certain frequencies to first locate, then isolate and reduce the noise. Chances are good it will only be a few orders of magnitude better and not perfect, but it should get the job done.