Hello @Gail1234 ,

Welcome to our community.

To quickly clarify the SOS indicator: on an iPhone, "SOS" near the Wi-Fi symbol means your phone has a Wi-Fi connection, but either has no internet access through it, or your cellular signal is unavailable. This is a general iOS status indicator and tells us the current Wi-Fi you're on doesn't have internet — it does not mean you're connected to the extender yet.

If you can't see the extender's Wi-Fi network: Since the Signal light is solid (green or blue), the extender may already be connected to your router. The extender's Wi-Fi name might be the same as your router's — check this guide to confirm or change it: How to Change Your TP-Link Range Extender Wi-Fi Password or Network Using Tether

If the Tether app is not finding the extender: 
Once you can see the extender's Wi-Fi, try these steps to get the Tether app working:
• Connect your iPhone to the extender's Wi-Fi network first, then search again in the Tether app.
• Turn off any VPN apps on your iPhone.
• Turn off cellular/mobile data on your iPhone.
• Go to Settings > Tether and make sure Local Network access is enabled — this is required for the Tether app to discover devices on iOS.
• Force close the Tether app (swipe it away) and relaunch it.
• If needed, unplug the extender for 30 seconds and plug it back in, then try again.

Start with the factory reset if you're not seeing the extender's Wi-Fi at all, as that's the most likely first step to get things back on track.