Am I required to offer expiation, after I pledged to God not to use the prayer beads (masbahah), but then I went back to using them because I felt remiss in remembrance (dhikr) without them?

Scholars differed concerning one who says: "I covenant with Allah to do such and such." The most correct opinion is that it is both an oath and a vow if he commits to it as an act of worship and obedience, and it is only an oath if he commits to it something that is not an act of worship, as advocated by Sheikh al-Islam Ibn Taymiyyah. So, if the covenant relates to abstaining from using the prayer beads (masbaha), which is permissible and not an act of worship, then the one who said it must offer expiation for an oath (kaffarat yameen) if he uses the prayer beads.