Hello, I'm Wes, and I'll be assisting you today.
Because the cartridge was inserted backwards, the only way to get it out is to try and force it out.
They can be pretty stuck when inserted backwards.
Try to wiggle the cartridge back and forth and side to side to get it loose. It will take some force to get it out.
If that does not work, use a flat head screwdriver to pry the ink cartridge out. Be sure to hold the carrier down so you don't pop that off either.
Let me know if you can get it loose.
Let me know if you run into any issues.
Also, please don't forget to rate my answer below so I can get credit for my work.
If you purchased the printer less than 1 year ago, you can get a replacement printer using the warranty.
Try to follow this step by step guide to show you how the cartridge should be inserted.
The name "Kodak" should be facing up.
Was the cartridge inserted the same way as in the link I sent you?