There are indeed boxes to contain your thunder at each designated campsite along with a fire ring.
https://www.fs.usda.gov/sites/nfs/files/r09/hiawatha/publication/BigIslandLakeWilderness_11x17Port_20250728.pdf
Also, here is a post from a few years go about that access:
https://bwca.com/index.cfm?fuseaction=forum.thread&threadId=1212235&forumID=121&confID=1&vt=1618386412
Found this post as I'm thinking of doing the same the with my family in a couple of weeks. I have paddled this area twice, both from the NW end, entering through Big Island Lake parking area and portaging/paddling in as far as Klondike. No usage fees last time I was there, but that was a...