Should I remove my SIM card before sending in my trade in phone?

You could. It doesn't have anything on it Apple could use. It just has information about your personal telephone service so I would. They only mention about removing them from Androids because they have more than service information, but Apple doesn't really need your card.

See What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Since we don't know where you are in the world. Here's Apple's various trade-in documents:

How to prepare your iPhone or Apple Watch for trade-in from Europe - Apple Support

How to prepare your iPhone, Apple Watch, or Android for trade-in - Apple Support

They both say: Remove the SIM card from your iPhone if it uses one and keep it in a safe place.

According to How to prepare your iPhone or Apple Watch for trade-in - Apple Support:

"Remove the SIM card from your iPhone if it uses one and keep it in a safe place."

Yes.

Thanks. Of course Apple's other document about trading in an iPhone does not say that—