We report the non-detection of dispersed bursts between 4 - 8 GHz from 2.5 hours of observations of FRB20200120E at 6 GHz using the Robert C. Byrd Green Bank Telescope. Our fluence limits are several times lower than the average burst fluences reported at 600 and 1400 MHz. We conclude that these non-detections are either due to high-frequency bursts being weaker and/or scintillation-induced modulated. It is also likely that our observations were non-concurrent with any activity window of FRB20200120E.