Quantizing is for MIDI. Ex; if you recorded a piano part or drum part played on a midi keyboard, and some notes were to far off the beat, you could 'quantize" the track or sections of the track to auto-majically move the midi notes to the nearest 1/4, 1/8th, 16th, 32nd beat.
On an audio track you can Snap To Grid in a similar fashion. But you will first need to find and mark or split at all the peaks. I'm not sure if RealBand or BIAB has these type of features. Different DAWs have various techniques for this.
The best way is as recommended by Charlie. Overdub, Punch In, or record several new tracks or Take Lanes then cut/copy/paste/merge the best parts to one or two keeper tracks.
Since my main instruments are vocal and guitar I tend to simply record the entire part several times until I like what I did and keep it. This reduces editing time. For me anyhow.

Does the noise in your head bother me ?