I hope they keep the "bastard blood, shed at war" line in the show.
I do understand people's bewilderment at Alicent mentioning their illegitimacy (there's a time and a place). I do get that if you happen to sympathise with Rhaenyra, this could easily be seen as audacious behaviour from Alicent. But just as I think people miss the point that Alicent was making about Jacaerys and Lucerys being two dragonriders that Rhaenyra herself let (if reluctantly) join her campaign whereas Jaehaerys was a defenceless seven year old who was killed while going to bed - I think people also miss another important reason as to why Alicent says this.
Even though they're both dead and Alicent is a captive by this point and has nothing to gain from it apart from threats of mutilation, she still refuses to swallow the fiction of their birth- or at least what she sincerely believes to be a lie. Fire and Blood is styled like a history book, and because we don't get first - hand accounts from Rhaenyra, we don't know if the rumors were true. (But let's be real, they were. George wrote it in a way that made it wayyy more likely that Harwin was the father. I think if he wanted to make the Strong boys' parentage ambiguous he could have had them all take after Rhaenyra and Laenor's Valyrian colouring while still keeping the open secret of Laenor's sexuality and Rhaenyra's closeness/attraction to Harwin Strong.)
The show is different in that it had Rhaenyra admit to Daemon that none of her sons are Laenor's. But what I find more interesting is that by episode 1.08, it is heavily implied that Jacaerys and Lucerys know it too. It's never said outright, nor do I think it ever was once during the time jump because doing so even just amongst themselves would have felt too dangerous. But them knowing the truth does add an interesting dimension. Jacaerys and Lucerys die fighting for their mother's incredibly shaky claim (if you're basing the Dance off the Anarchy, then yes it is shaky sorry) but by extension they also die fighting for their own claims - which according to the rules of their society, they have no right to. It is the same rules that they would enforce. There IS a hypocrisy, and as much as I do agree with @lemonhemlock when they say that it's annoying/unfair that only Rhaenyra's children with Daemon got to live, I think it is telling that all three of the sons that she intended to inherit after her all ended up being killed. The son of hers that does end up inheriting the Iron Throne after her death is the trueborn Aegon the Younger, but it's as Aegon II's heir.
So from Alicent's perspective... it is very possible that in her anger, she made the comments because she believed Jacaerys and Lucerys died fighting for something they knew didn't belong to them, and thus their deaths were deserved/be seen as narrative punishment to the reader. Why should she feel sorry for two people who in her eyes, would be usurpers?
