Why did Starks and Boltons attacked Three Sisters?
The pretext seems to have been to stop their piracy, which sometimes escalated into more than just raiding ships:
Lord Godric's forebears had been pirate kings until the Starks came down on them with fire and sword. —Davos I ADWD
Reavers from the Three Sisters took [the Wolf’s Den at what is now White Harbor] once, making it their toehold in the north. During the wars between Winterfell and the Vale, it was besieged by Osgood Arryn, the Old Falcon, and burned by his son, the one remembered as the Talon. —Davos IV
The last isles to be wedded to the Vale were the Three Sisters. For thousands of years, these islands had boasted their own cruel kings, pirates and raiders whose longships sailed the Bite, the narrow sea, and even the Shivering Sea with impunity, plundering and reaving as they would and returning to the Sisters laden with gold and slaves.
These depredations finally led the Kings of Winter to send their own war fleets to seek dominion over the Sisters—for whoever holds the Three Sisters holds the Bite. —TWOIAF: The Vale
However, the mention of the Three Sisters being a way to control the Bite, as well as the brutality that went on for a thousand years in “The Worthless War”, indicates it was more a conquest campaign to control shipping in the Bite and use the islands as a buffer zone between the North and the Vale, and perhaps sinisterly, to repopulate the isles with loyal Northmen. “The maesters say the Rape of the Three Sisters was two thousand years ago, but Sisterton has not forgotten. We were a free people before that, with our kings ruling over us. Afterward, we had to bend our knees to the Eyrie to get the northmen out. The wolf and the falcon fought over us for a thousand years, till between the two of them they had gnawed all the fat and flesh off the bones of these poor islands.” Maybe it started out as a punitive expedition with economic goals, but it ended as part vanity campaign, part resettling effort as the Northern occupation of the Sisters lasted 1000 years.
If you’re wondering why Borrell and family have the mark—aka webbing between the toes—it’s to parallel them to the crannogmen, also rumored “to have webbed hands and feet like frogs” —TWOIAF: The Crannogmen of The Neck, because they were both independent border kingdoms that the North wanted to conquer and live in unique fashion to their neighbors. What they failed with the Sisters, they succeeded under Rickard Stark who killed the last Marsh King and wed his daughter.