Removing all the sticky stuff may take a few minutes and more than one application of the Goo Gone but the bottle will be squeaky clean once it's cleaned up and rinsed off.
Once all the adhesive is wiped off the Smartwater bottle, run the bottle under some hot tapwater until the Goo Gone residue is washed off. The plastic should look and feel clean.

Dry the bottle off with a clean rag or paper towel.
Using the same process of marking and cutting, cut the top of the parmesan cheese bottle about one inch below the screw-on cap.
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do-it-yourself aquarium and semi-aquatic background designs beyond the traditional
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Using a straight edge ruler and magic marker, make a line around the bottle about 5 inches from the bottom.

In this photo some lumber was used to make an L shaped frame to make it easier to make a straight line around the bottle.

The base of the bottle rests on the lower section of the L shaped frame and the bottle is simply turned with the marker being held in place.

The black notches on the frame are one inch apart each.
Using the utility razor, carefully cut the bottle along the marked line.

The wood frame also helps with this step but is not required.
DIY Water Bottle Power Filter with Screw on Cap
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This project idea is an improvement on the original DIY water bottle power filter design. The goal was to make the filter safer for long-term use around smaller fish.