。
She used a damp cloth to wipe off the dust.
Literal
She [topic-は] dust [object-を] wipe [for-the-purpose-of-のに] damp cloth [object-を] used.
のに here is the purposive のに ('for the purpose of, in order to'), not the concessive のに ('despite, even though') — context distinguishes the two. The purposive のに attaches a verb's plain form to a verb of using/needing/taking time, framing the activity as the goal: 'used a damp cloth for the purpose of wiping the dust.' 拭う is a slightly more deliberate, written-flavored verb than 拭く — both mean 'wipe,' but 拭う is more common with abstract objects (涙を拭う 'wipe away tears') and adds a touch of literary tone.