I presume the basement is unfinished.
If that is correct, then it is forbidden under the code to remove that GFCI.
Even if you install a dedicated receptacle for the freezer, it would still need a GFCI. Get a freezer alarm (less than $20).

There were some exceptions under the 2008 NEC. Not sure if they exist under the current NEC.

(5) Unfinished basements � for purposes of this section, unfinished basements are defined as portions or areas of the basement not intended as habitable rooms and limited to storage areas, work areas, and the like
Exception No. 1 to (5): Receptacles that are not readily accessible.
Exception No. 2 to (5): A single receptacle or a duplex receptacle for two appliances located within dedicated space for each appliance that, in normal use, is not easily moved from one place to another and that is cord-and-plug connected in accordance with 400.8(A)(6), (A)(8), or (A)().

Here is a link that might be useful: Source of cited NEC text

Those exceptions were not included in the 2011 NEC.

I don't know where they got that CITE from but it's NOT from either the 2008 or 2011 NEC.

Here's the exact verbiage of that passage lifted straight from the NEC text itself:

(5) Unfinished basements � for purposes of this section, unfinished basements are defined as portions or areas of the basement not intended as habitable rooms and limited to storage areas, work areas, and the like See related Illustration Staff Note

Exception to (5): A receptacle supplying only a permanently installed fire alarm or burglar alarm system shall not be required to have ground-fault circuit-interrupter protection.

As you see, there is only one exception to the unfinished basement clause and it applies to alarms.

In fact, to find that text you have to go back to the 2005 code.

The non-normative text in the 2008 and later codes even specifically show the freezer plugged into the GFCI.

Good god, NEVER EVER EVER take code information from a housing inspection business.

FYI the Chaney Instrument 00985 Wireless Refrigerator Freezer Thermometer Alarm is an inexpensive set and works well. (The batteries are expensive, though, since you need Li for the sensors.) I would probably combine it with an a alarm that plugs into the second outlet and squawks when the power goes off, also inexpensive. It will alert you before the freezer warms up better preserving your food quality.

Put a light that used used daily on the circuit with the freezer.

Better to notice the power is out than that the freezer has started to warm.

One of my favorites has always been the kitchen ceiling light.
You will be sure to notice it not working.

You can get for $15 a combo flashlight and beeper that lets you know when the power on a receptacle has failed. If the basement is more out of the way than you would notice that a louder one (91db) can be head for a bit more money.

Whether you put in a GFCI or not, the breaker can still trip so having the alarm or light or something is a good idea.

I'd still get a freezer alarm as well. I lost a lot of food once when the door somehow was left or came ajar on the one I've got in the garage.