@Floatflyer 

What is the model of the range extender that you are using?

It is a TL-WA855RE.  I did a live chat and the tech asked me to move the extender to another outlet and I did that.  To my surprise and delight, the phones do not seem to be affected by this new location which is only 6-7 ft away, go figure.  I completed the WPS buttons pushing to complete the installation and phones remain in service.  I have not determined if I actually have "extended range" or not.

@Floatflyer 

The extender does operate on the same frequency (2.4GHz) as the cordless phones so it can interfere which seemed like it was, but good that both work now.

As far as the extender itself, look at the signal light. If it is connected to your router, the LED will be solid blue. If it is solid red it is too far from the router.

The wireless network should have a _ext at the end of it so if your Wi-Fi is mywifi, you should now see in addition to that mywifi_ext. That will be your extender that you connect to.

If your TL-W855RE is hardware version 4, it will add _ext. If your extender is hardware version 3, the network name will be the same as your router.

To find the version you can look on the box label or behind the extender.