〜て + 置く

is used to imply that an action is in preparation of something in the future. It comes from て置く, 'putting something ready (in advance)'

テストの復習しておく I will review the test (for the future)

日本語の辞書を買っておいた I bought/will buy a japanese dictionary (in anticipation of needing it in the future)

車を修理しておきます I will repair the car (for future use)

といて is a request for someone to do something in advance.

~とく Abbreviation

止めておこう 止めとこう。 Let's stop (before it gets out of hand)

https://www.imabi.net/teoku.htm