I really like the design of the original thing, but once you fix it in place it's not gonna be easily removable, definitely not for routine cleaning.
I imagined the inside of the bottom half of the holder might get really gross maybe 1 or 2 years down the line. Definitely not somewhere I'd personally want to store something that goes in my mouth into.

My version is heavily derivative of the original, but designed to be more easily cleaned.
It's made up of two mounting frames that will be semi-permanently attached to whatever surface you want this mounted onto through double sided tape, as well as two removable inner parts that slot into the frames, and will be the one in physical contact with the straws. This way you can just put them in the dishwasher every now and then.

Other things I changed:

• Added a 0.4mm deep recess on the back to compensate for the thickness of double-sided tape. The whole thing will sit more flush to the surface it's mounted onto.
• Changed the floor of the bottom tray from holes to a grid design for better drainage
• Moved the pipe cleaner holders so it's one per side instead of two on one side. I like symmetry.
• Added a chamfer to the front corners, which is scientifically proven to make any design 14% sexier.

Make sure you print "inner tray" and "top spacer" out of PETG to make them dishwasher-safe and (relatively) food-safe. That's the whole point after all, right? Also make sure you don't print the outer frames of PETG as double sided tape might not stick too well on them. I used PLA for the outer frame, ABS would be fine too.