Answer

Who is “Varda,” and where is her pilpul?
What you remember is not the Sha’agat Aryeh but the Avnei Nezer. He explains why the Sefer HaChinukh writes that women are exempt from wiping out Amalek but obligated in the war against the seven nations. The explanation he offers is that killing the seven nations is done so that we not seek them out unnecessarily—so that they not cause us to stumble in idolatry—and therefore killing them on the Sabbath is permitted, since it is like a labor not needed for its own purpose (as with killing a snake so that it will not bite us, and the like). Consequently, the commandment is not time-bound, and women are obligated in it. But killing Amalek is needed for its own purpose, and therefore is forbidden on the Sabbath, so it is a time-bound positive commandment and women are exempt.
Another pilpul is the obligation of a doorpost in tzitzit: if a four-cornered garment, which is exempt from mezuzah, is obligated in tzitzit, then a doorpost, which is obligated in mezuzah, all the more so should be obligated in tzitzit! And similarly regarding the obligation of a four-cornered garment in mezuzah.