In 1-quart saucepan, place water; sprinkle with gelatin; let stand 1 minute. Heat over low heat, about 2 minutes, stirring constantly, until gelatin is dissolved. Cool slightly.
In medium bowl, beat cream cheese with electric mixer on medium speed until smooth. Add yogurt and gelatin mixture; beat on low speed until well blended. Fold in whipped topping. Spoon into crust. Refrigerate until set, about 2 hours.
Before serving, garnish pie with additional whipped topping and sliced strawberries.