The correct alternative to fill in the blank is: "off" OPTION 3

The sentence would be: "Take your shoes off when you enter the house."

The correct alternative, "off," is used to indicate the action of removing or taking away something. In this context, when someone enters the house, the expectation is for them to remove their shoes. Therefore, the correct and idiomatic phrasing is "Take your shoes off when you enter the house."