I'm not clear what you exactly want to do, to restore a known sine (phase, frequency, etc.) from a noisy signal containing glitches or to remove these glitches to find the "original" low frequency signal, which need not necessarily to be a sine?

In all cases, if the glitches cannot be characterized as regular noise (i.g. Gaussian noise), means if only glitches of same polarity occur, then you have no chance to restore the "original" waveform by any sort of filtering. Even a least squares fit will not work, if you only expect a sine or a Fourier sum of sines making up your samples.

You should detect the glitches and subtract them from the noisy signal. A du/dt-filter can help to find them in the samples.
Try to fabricate these glitches in your laboratory and find their typical waveform, so that you can first order detect them in your samples and subtract them from the signal.

Another idea is to do a FFT followed by a subsequent Fourier synthesis, but omitting the harmonics representing the glitches. This will only work, of course, if the according spectra are enough separated.

Kai