Intransitive to strip off usually means remove [all of] one's clothes, but when strip is used transitively (with the "object" being either some outer covering being removed, or the thing that covered is removed from), off is often effectively an optional preposition...
1: He used a scraper to strip off the old paint from the wall
2: He used a scraper to strip the old paint from the wall
3: He used a scraper to strip the old paint off the wall
...where all the above are perfectly valid ways of saying the same thing (note that in #1, of primarily couples with strip, but in #3 it couples with the wall as an alternative to from).
But - suppose I wanted to say only half the paint was removed? In that context we also have to note that of is effectively an optional preposition in half of the paint. Arguably this is somewhat unfortunate for learners, but all the examples below are also perfectly valid...
4: He used a scraper to strip off half the old paint from the wall
5: He used a scraper to strip half the old paint from the wall
6: He used a scraper to strip half the old paint off the wall
7: He used a scraper to strip off half of the old paint from the wall
8: He used a scraper to strip half of the old paint from the wall
9: He used a scraper to strip half of the old paint off the wall
Technically speaking,...
10: He used a scraper to strip off half of the old paint off the wall
...is also "more or less" valid. But it's very clumsy, so people would rarely use that one.
In short, both of OP's possibilities are valid, as are You have stripped off half of its gear (both prepositions) AND ...stripped half its gear (neither preposition).