4. It Actually Doesn't Affect The Story All That Much
In the books, Triss has three main roles. The first is the aforementioned training of Ciri at Kaer Morhen, then there's her membership to the Lodge of Sorceresses and, finally, there's her romance with Geralt.
As the leaked synopsis for season two reads like this:
Convinced Yennefer’s life was lost at the Battle of Sodden, Geralt of Rivia brings Princess Cirilla to the safest place he knows, his childhood home of Kaer Morhen. While the Continent’s kings, elves, humans and demons strive for supremacy outside its walls, he must protect the girl from something far more dangerous: the mysterious power she possesses inside.
It is fairly logical for Geralt to turn to Triss Merigold for help with Ciri, regardless of them not being romantically entangled (given her help with Foltest's striga). Contacting Triss might not even be an option for Geralt if he believes Yennefer to be dead, seeing as Triss fought at the Battle of Sodden too, so this aspect of her character might have already hit the cutting room floor anyway.
As for her joining the Lodge of Sorceresses - that has practically nothing to do with her relationship with Geralt as, again, he can still trust her without them having slept with each other.
In essence, the biggest 'story' changes replacing Triss in the love triangle would have is that there would be no sex scenes between her and Geralt and the show wouldn't really fit into the canon established in the games. Yet, considering how the former of these problems can be remedied by a quick internet search and the latter would only be an issue for those who love the games and the Netflix series but refuse to read the books, these problems are solely superficial.