・・・

Apparently, my previous dentist said that if I quit smoking, he'd clean the tar off my teeth... or so I heard.

Literal

Previous dentist-honorific [target-に], tobacco [object-を] quit [conditional-なら], tar-removal do-give... [quotative-と] say-passive [hearsay-そうです].

Several layers here. ~そうです at the end is the hearsay 'I heard that,' marking the whole sentence as secondhand information. Note this is distinct from the appearance-そう (_そうだ after adjective stems). Inside, 言われた is passive, so 'was told by.' The quoted conditional offer uses ~てあげる as a benefactive. ヤニ ('nicotine tar, pitch, resin') is written in katakana, a choice that visually marks it as a substance. The trailing ・・・ softens the declaration.