"The part of her remarks most likely to be politically problematic concern financial industry regulation" is a complete sentence. The verb is "concern", the subject is everything before "concern", and the object is everything after it. "The part of her remarks most likely to be politically problematic concerning financial industry regulation" is not a complete sentence as it does not have a main (finite) verb.
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takafromtokyoThen, if I make it simple, shouldn't it be, "The part of her remarks concerns financial industry regulation"?That is a grammatically possible sentence, but you have lost most of the meaning, and point, of the original. Also, to be idiomatic in this context, "The part of" needs to be changed to "Part of" or "A part of".