We use reconstructed star-formation histories (SFHs) of quiescent galaxies at z = 0.6 − 1 in the LEGA-C survey to identify secondary star-formation episodes that, after an initial period of quiescence, moved the galaxies back to the star-forming main sequence (blue cloud). 16 ± 3% of the z ∼ 0.8 quiescent population has experienced such rejuvenation events in the redshift range 0.7 < z < 1.5 after reaching quiescence at some earlier time. On average, these galaxies first became quiescent at z = 1.2, and those that rejuvenated, remained quiescent for ∼ 1Gyr before their secondary SF episode which lasted ∼ 0.7Gyr. The stellar mass attributed to rejuvenation is on average 10% of the galaxy stellar mass, with rare instances of an increase of more than a factor 2. Overall, rejuvenation events only contribute ∼ 2% of the total stellar mass in z ∼ 0.8 quiescent galaxies and we conclude that rejuvenation is not an important evolutionary channel when considering the growth of the red sequence. However, our results complicate the interpretation of galaxy demographics in color space: the galaxies with rejuvenation events tend to lie in the so-called 'green valley', yet their progenitors were quiescent at z ∼ 2.