Previous research has demonstrated that rapeseed sprouts obtained under salinity demonstrate greater phenolic content and antioxidant activity compared to those sprouted with distilled water. This work aimed to test the hypothesis that these effects of salinity may persist into the next generation, so that offspring seeds of plants grown under salt stress may give edible sprouts with increased phenolic content and antioxidant activity. Plants of one rapeseed cultivar were grown in pots with 0, 100 and 200 mM NaCl, isolated from each other at flowering to prevent cross-pollination. Offspring seeds harvested from each salinity treatment were then sprouted with distilled water. We performed the extraction of free and bound phenolic fractions of sprouts and, in each fraction (methanolic extract), we determined the total polyphenols (P), flavonoids, (F), and tannins (T) with Folin–Ciocalteu reagent, the phenolic acids (PAs) by ultra-high-performance liquid chromatographs (UHPLC) analysis, and the antioxidant activity with three tests (2,2-diphenyl-1-picrylhydrazyl-hydrate, DPPH; ferric reducing antioxidant power, FRAP; 2,2′-azino-bis[3-ethylbenzothiazoline-6-sulfonic acid] diammonium salt, ABTS). Individual seed weight was slightly decreased by salinity, whereas germination performance was improved, with a lower mean germination time for salted treatments. No significant differences were observed among treatments for P, F and T, except for bound P, while, in most cases, single PAs (as free, bound and total fractions) and antioxidant activity were significantly increased in salted treatments. Our results open new perspectives for the elicitation of secondary metabolites in the offspring seeds by growing parental plants under stressing conditions, imposed on purpose or naturally occurring.