Preheat the oven to 350°F.
Grease a 9x9-inch baking pan with nonstick cooking spray or butter.
Set the prepared pan aside.
Place the room-temperature butter, granulated sugar, and eggs in a large mixing bowl.
Beat the ingredients together until the mixture is smooth and well combined.
Add the vanilla extract.
Add the lime zest.
Mix until the vanilla and lime zest are evenly incorporated.
In a separate small bowl, combine the all-purpose flour, salt, and baking powder.
Sift or whisk the dry ingredients until fully combined.
Gradually add the dry ingredients to the wet mixture.
Add the chopped maraschino cherries.
Mix only until the ingredients are just combined.
Do not overmix the batter.
Transfer the batter to the prepared baking pan.
Spread the batter evenly into the pan with a spatula.
Place the pan in the preheated oven.
Bake for 16 to 18 minutes, or until a toothpick inserted into the center comes out clean.
Remove the pan from the oven.
Allow the bars to cool completely before frosting.
To prepare the frosting, place the softened cream cheese and room-temperature butter in a large mixing bowl.
Beat until smooth and creamy.
Add the grenadine syrup.
Add the maraschino cherry juice.
Add 1 cup of powdered sugar.
Beat until the frosting is smooth and spreadable.
Add up to 1/2 cup additional powdered sugar, if a thicker frosting is desired.
Refrigerate the frosting until ready to use, if necessary.
Spread the frosting evenly over the fully cooled bars.
Chill the frosted bars until ready to serve.
Slice into 12 bars.
Serve chilled or slightly softened.