This study deals with the telemonitoring, with a connected tensiometer, of 16 patients treated for a kidney cancer. Each one of these patients recorded his/her blood pressure at home during 63 days and the data was sent to his/her medical doctor. At the same time they were treated with antihypertensive medication when necessary. In this work, our goal was to analyze the complexity of the blood pressure time series. For this purpose, we proposed to use the refined composite multiscale entropy (RCMSE) measures. Our results show that the patterns of RCMSE through temporal scales evolve with the antihypertensive medication. The later might therefore have an impact on home-acquired blood pressure complexity. RCMSE could therefore be an interesting information theory-based tool to study home-acquired physiological data.