Hi there MakingMemories391,
If you are getting this error when inviting people to a Calendar event, let's first see if this continues when you are connected to a Wi-Fi network. This will help us isolate whether the network connection or something else is responsible for what's occurring.
If this happens on multiple network connections, then let's next ensure that your iPhone is fully updated. This installs feature improvements and bug fixes that can resolve unexpected behavior like this. These steps from Update your iPhone or iPad show how to back up and update:
1. Back up your device using iCloud or your computer.
2. Plug your device into power and connect to the internet with Wi-Fi.
3. Go to Settings > General, then tap Software Update.
4. If you see more than one software update option available, choose the one that you want to install.
5. Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do.
Cheers!