Do I need to remove the paper stuck in these cartridges?

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No, nothing needs to be removed. Please make sure to not take off or pierce the plastic covering the cartridge shown 

Just take out the cartridges from the plastic bag, then push them into the printer. The printer will pierce this plastic for you, as otherwise the ink could leak out of the cartridge. It it meant to be installed as such, and may need a little extra pushing than expected.