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Tunneling spectroscopy was performed on Nb pieces prepared by the same processes used to etch and clean superconducting radio frequency (SRF) cavities. Air exposed, electropolished Nb exhibited a surface superconducting gap
Δ
=
1.55
meV
, which is characteristic of a clean, bulk Nb. However, the tunneling density of states (DOS) was significantly broadened. The Nb pieces, which were treated with the same mild baking used to improve the
Q
slope in SRF cavities, reveal a sharper DOS. Good fits to the DOS were obtained by using the Shiba theory, suggesting that magnetic scattering of quasiparticles is the origin of the gapless surface superconductivity and a heretofore unrecognized contributor to the
Q
-slope problem of Nb SRF cavities.