A quick thrown-together bandpass filter is shown in the schematic. The base frequency is not in the middle of the filter response , but the filter suffices because we only care about eliminating DC and the higher harmonics, and attenuating the generated frequency to match the original chirp. At 276khz, the filter attenuates the fundamental frequency to 186mVp-p, and the 3rd harmonic is down at 24mVp-p which is sufficient for my purposes.