Hi lori.l.schelin,
Welcome to Apple Support Communities. While there isn't a direct method for printing a text message thread, we would like to offer a way to achieve this.
Assuming you have a method to print from your iPhone, you could take a screenshot of the messages and then print those. Here's how:Take a screenshot on your iPhone - Apple Support "How to take a screenshot on iPhone 13 and other models with Face IDPress the side button and the volume up button at the same time.
Quickly release both buttons.After you take a screenshot, a thumbnail temporarily appears in the lower-left corner of your screen. Tap the thumbnail to open it or swipe left to dismiss it.
How to take a screenshot on iPhone models with Touch ID and side buttonPress the side button and the Home button at the same time.
Quickly release both buttons.After you take a screenshot, a thumbnail temporarily appears in the lower-left corner of your screen. Tap the thumbnail to open it or swipe left to dismiss it.
How to take a screenshot on iPhone models with Touch ID and top buttonPress the top button and the Home button at the same time.
Quickly release both buttons.After you take a screenshot, a thumbnail temporarily appears in the lower-left corner of your screen. Tap the thumbnail to open it or swipe left to dismiss it."
To print from your iPhone:Use AirPrint to print from your iPhone, iPad, or iPod touch - Apple Support
"Open the app that you want to print from.To find the print option, tap the app’s share icon — 
or 
— or tap 
.Scroll down and tap 
or Print. If you can’t find the print option, check the app’s User Guide or Help section. Not all apps support AirPrint.Tap Select Printer and choose an AirPrint-enabled printer. Choose the number of copies or other options, like which pages you want to print.Tap Print in the upper-right corner."
For this method you will need an AirPrint-enabled printer as mentioned in the resource above.
We hope this helps.
Cheers!
