I've encountered many verbs with 「取り~」 inserted. Up till now I've treated 「取り+verb」 as separate vocabulary, but quite often, the definitions are not much different than the base verb alone. In certain uses, 「取り+verb」 seems more common and thus may be more natural to native speakers. I'd like to clarify how I should interpret these.
On dictionary.goo.ne.jp, this definition for 「取り」 is 「動詞などに付いて、語調を整え、改まった感じにするのに用いる。」which says that it just adds a formal feeling to a verb and doesn't change the meaning. But that doesn't seem like a complete explanation.
Some examples I've encountered:
仕切る → 取り仕切る
調べる → 取り調べる
揃える → 取り揃える
立てる → 取り立てる
付く・付ける → 取り付く・取り付ける
残す → 取り残す
戻す → 取り戻す
寄せる → 取り寄せる