As Andy says, BeSS standard practise is to leave the telluric lines in when submitting to the database. When analysing spectra though you will want to remove them and it is quite possible for amateurs to do this.
For high resolution spectra where the individual lines are visible it is quite straightforward using a standard template for O2 and H2O lines which is scaled to fit the magnitude of the lines. Some software eg ISIS Visual spec have this function built in.
For low resolution spectra it is more difficult as the lines blend into broad bands. The same technique can be used though by producing your own low resolution template. This is done by taking spectra of a hot star at two different air masses. If you divide one by the other, the result is the extra atmospheric absorption due to the additional atmosphere. This can then be used as a template to remove the telluric bands. You can see a simple example of using a low resolution template in this poster paper
(This technique of measuring stars at different air masses is used by professionals (and sometimes by amateurs) to correct for all atmospheric effects including extinction rather than trying to match the air mass of reference star as is commonly used by amateurs. Correction for extinction (rather than just the telluric bands) using this technique though needs photometric skies so the atmospheric conditions do not change between the two measurements at different air masses.