I would suggest that if you are unsure what to do then a factory reset might be the best way to go.
Otherwise when you try to connect wirelessly to the extender the PC will have ‘limited connectivity’, it will not have a LAN IP address because there is no communication with a DHCP server (the router). But even in that case the URL that you use to access the extender should still work e.g. http://mywifiext.net (or whatever the User Manual suggests). From there you should be able to log into the extender and following the instructions in the User Manual scan for your new router WiFi and enter the new WiFi passphrase.
One other option of course, is to set up the new router’s WiFi to match the old, i.e. the same network name (SSID) and passphase, the extender should then automatically connect to the new router.
