In this paper, we study backward stochastic Volterra integral equations introduced in Lin [Stochastic Anal. Appl. 20 (2002) 165–183] and Yong [Stochastic Process. Appl. 116 (2006) 779–795] and extend the existence, uniqueness or comparison results for general filtration as in Papapantoleon et al. [Electron. J. Probab. 23 (2018) EJP240] (not only Brownian-Poisson setting). We also consider Lp-data and explore the time regularity of the solution in the Itô setting, which is also new in this jump setting.