In a medium bowl, mix together cream cheese and confectioners' sugar until smooth and creamy. Stir in vanilla and almond extract. In a separate bowl, whip cream until peaks form. Fold into cream cheese mixture. Spread over bottom of baked pie shell. Chill.
In a saucepan, mix together sugar and cornstarch. Stir in water until smooth. Add grenadine and lemon juice. Bring to a boil over medium heat. Cook 5 minutes, stirring constantly, or until thickened. Allow to cool, then chill.
Just before serving, stir together strawberries and cooled cornstarch mixture until evenly coated. Spread over cream cheese layer.