I think ConservativeMind has the best answer so far. Advertised speeds refer the Ethernet so you need to test your speed using a Ethernet directly to the router. And note that range extenders reduce speed, and wireless does far more.
See answers to Do WiFi repeaters/range extenders reduce Internet speed?
The choke point is the range extender itself. Silly me for assuming that a range extender which claimed it was for high speed internet would be for high speed internet.
I have posted in the TP-Link technical support forum to find out if they sell a range extender with a high speed RJ45 output jack.
Thanks for all of the help. FReepers rule!