Pretty astounding, isn't it? I don't see a paper, but there was a webinar [1]. There's a technical synopsis at 8:00. The phenomenon they're measuring is actually signficant. It's the total number of (free?) electrons between the satellite and the receiver. Typically its about 10^12 electrons/m^3 (@8:00 in video). The disturbance from the 2011 earthquake and tsunami was, if I'm reading the movie/chart correctly, about +/- 1 TECU, which is 10^16 electrons/m^3 (@10:40). The water elevation may only be a few feet in open ocean, but it's over a vast area. That's a lot of power.
They're measuring it by looking for phase differences in the received L-band (~2GHz) signals, rather than amplitude. That eliminates lots of noise. And they're looking for a particular pattern, which lets you get way below the noise floor. For example, the signal strength of the GNSS (GPS) signal itself might be -125 dBm, while the noise level is -110 dBm [2]. That means the signal is 10^-12 _milliwatts_, and the noise is about 30 times larger. But by looking for a pattern the receiver gets a 43 dB processing boost, putting the effective signal well above the noise.