Oh, so it wasn't as shown... well that would explain that, wouldn't it.
So what's the problem with the noise? Like I said, sensitivity goes up with Q, and so does gain, so you can afford larger R402. I have no idea what your sensor is/does/looks like, if it's susceptible to ambient noise, or can't easily be changed to increase Q, or what.
The noise on the scope, may or may not be there in circuit. Scopes typically have in the ballpark of 1mV RMS noise. That looks a bit more than that, I don't know. Noise can be present due to ambient sources (faulty SMPS, radio transmitters), or other sources in the circuit (parasitic oscillation, or anything else really).
Noise can even be present in the circuit, without appearing across the nodes you think you're measuring, and still show up on the scope (or while probing) -- common mode noise (voltage between circuit ground, and scope ground or other surroundings) manifests in this way. The trick is you'll see CM noise when probing ground itself (probe tip to ground, clip open; or even with clip and tip both grounded, particularly at higher frequencies).
Noise can be filtered, say by adding another R-(L||C) after this one, at modest expense to Q and gain, or with an active filter (including, or after, the buffer; note that noise can then affect the buffer, which may be undesirable).
Since you have the excitation source, you can also sense it synchronously, which would consist of using a PLL to double the frequency, then a flip-flop to halve it, and a few gates to generate quadrature pulses. (A phase shift network could also be used, if the frequency range is narrow.) The quadrature clocks drive pairs of analog switches which pass or invert the signal (after the buffer), and the results are filtered (averaged). This gives the I and Q components of the analytical signal, which can be used directly as a complex number (I + jQ), or processed further (e.g. atan2(Q, I) to get the argument aka phase angle), which probably isn't too useful for analog purposes (that's a complex function), but can be done digitally. This has the advantage of extreme sensitivity (lock-in amplifiers use this or related techniques to very high sensitivity indeed), freedom from spurious modes (as the XOR phase detector may give) and freedom from edge sensitivity (as an edge-sensitive (type 2) phase detector has). The downside is the complexity, which should be very much overkill for a simple problem like this -- but again, as I have no idea what you're doing, it might pay off to see adjacent approaches.
Tim