There are two questions here: What is it? Does it work?
What Is It?
Your dietitian is using Applied Kinesiology.
Example of the claim:
Applied kinesiology may be used to detect allergies and sensitivities to a variety of substances including foods, dustmites, pollens, vaccinations and many medications. When exposed to an allergen, the theory is that the muscle will weaken to indicate an allergy. To test for this weakness, the client will hold their arm out horizontally whilst holding the suspected allergen. The kinesiologist will then test the arm for weakness or strength by trying to push it down, usually from the wrist.
Don't get it confused with kinesiology:
Applied kinesiology should be distinguished from kinesiology (biomechanics), which is the scientific study of movement." Unfortunately, some professionals and educators refer to science-based kinesiology as "applied kinesiology," which increases the risk that people searching for information will confuse the two.
Does it Work?
- Three practitioners testing eleven subjects made significantly different assessments; their diagnoses of nutritional deficiencies did not correspond to the nutrient levels obtain by blood serum analysis; and that the responses to nutrient substances did not significantly differ from responses to placebos .
- Another study found no effect from administering the nutrients "expected" to strengthen a muscle diagnosed as "weak" by AK practitioners." 
- Researchers who conducted an elaborate double-blind trial concluded that "muscle response appeared to be a random phenomenon." 
- Another study showed that suggestion can influence the outcome of muscle-testing. During part of this experiment, college students were told that chewing M&M candies would give them instant energy that would probably make them test stronger. Five out of nine did so .
- Four AK practitioners tested seven patients who were extremely sensitive to wasp venom. Altogether, 140 muscle tests were done to see how the patients responded to preparations of venom or salt water in a bottle. If the test were valid, the venom bottles should result in "strong" reactions and the salt-water bottles should produce "weak" test reactions. However, the practitioners were unable to identify which bottles contained which .
- Several chiropractors were tested at a medical office while under unblinded and blinded conditions. During the volunteers could resist downward pressure when a drop of glucose was placed on their tongue but could resist when fructose was administered. The the arm tests were repeated using substances in coded test tubes so that the volunteer, the chiropractors, and the onlookers could not tell which solution being applied to the volunteer's tongue. When the code was revealed, There was no connection between ability to resist and whether the volunteer was given the "good" or the "bad" sugar .
In conclusion, it's time to find a new dietitian, and to consider complaining about the current one to their licensing body.