It's perfectly okay to pee with the tampon inside you and there's no need to remove the tampon to pee since the tampon is inserted into the second part and the pee comes out the first part.
When peeing with a tampon in you can move the string to the tampon out of the way however you can still pee with the tampon in.
The tampon goes into your vagina to absorb menstrual fluid so having the tampon in won't disrupt your ability to urinate.
Just move the string to the tampon out of the way before peeing and it will be okay.
I've peed a lot with the tampon in and nothing bad has happened.