This is kind of a tricky one and I'd suggest you ask your CPA how to set that up since technically bartering is a form of payment.  

You can ring it up and then use other payment on the virtual terminal.

Or create a discount code and name it something I use MARKETING and make it a 100% discount.  That will take the item out of inventory and then I use the marketing total at the end of the year for taxes.  

I've used the COMP option at checkout.

https://squareup.com/help/us/en/article/5814-get-started-with-comp-and-void

This reduces the cost to zero, and this will keep your inventory current. But as far as tax implications....I can't offer advice on that subject.

You could also do as @Doran mentioned and use this as an advertising/marketing expense, because you're basically using the items for those purposes (to get the word out about you and your publications.) Good luck to you! Thanks for joining us in the Square Seller Community!