Hi Deborah,
I see very little indication that the newer term is gaining any acceptance. Found only two references using the term, both from 2018. 

1) THE SIGNS OF MITE DAMAGE- HOW TO IDENTIFY PROGRESSED VARROOSIS? SEPTEMBER 26, 2018 BY GARETT SLATER
https://beeinformed.org/2018/09/26/the-signs-of-mite-damage-how-to-identify-progressed-varroosis/

> Deformed Wing Virus (DWV) and Varroa Mite Syndrome (formerly Parasitic Mite Syndrome or PMS) can signify high mite levels.  

2) Mathialagan, M., Johnson, Y., & Thangaraj, E. (2018). Isolation, characterization and identification of probiotic lactic acid bacteria (LAB) from honey bees. International journal of current microbiology and applied sciences, 7, 849-906.

> At present, acaricides and antibiotics are extensively used in apiculture to manage the ectoparasitic Varroa mite syndrome. 

Fact is, the older term is falling into disuse, as well. I found six uses of it in 2019.  I think these citations lend credibility to the continued use of "PMS," to which some may object on non-scientific grounds (it sounds bad), but also the lack of use perhaps indicates the lack of usefulness. I think there is a good case for ditching PMS along with CCD. 

1) Grooming behavior and gene expression of the Indiana “mite-biter” honey bee stock
N Morfin, K Given, M Evans, E Guzman-Novoa… - Apidologie, 2019 - Springer

> These colonies were highly infested with mites and had bees with deformed wings and signs of brood diseases such as chalk brood and European foulbrood that looked typical of parasitic mite syndrome

2) Lee, K. V., Goblirsch, M., McDermott, E., Tarpy, D. R., & Spivak, M. (2019). Is the brood pattern within a honey bee colony a reliable indicator of queen quality?. Insects, 10(1), 12.

> American foulbrood (Paenibacillus larvae), European foulbrood (Melissococcus plutonius), chalkbrood (Ascosphaera apis), sacbrood virus, hive beetles (Aethina tumida), wax moth (Gallaria melonella), V. destructor mites, deformed wings, and parasitic mite syndrome

By the way, "Idiopathic brood disease syndrome" didn't really catch on, either:

Tarpy, D. R., Lengerich, E. J., & Pettis, J. S. (2013). Idiopathic brood disease syndrome and queen events as precursors of colony mortality in migratory beekeeping operations in the eastern United States. Preventive veterinary medicine, 108(2-3), 225-233.
Chicago	

This term apparently originated with van Englesdorp's PhD Thesis:

VanEngelsdorp, D. (2011). Morbidity and Mortality in the Bee Yard.
> clinical symptoms of Idiopathic Brood Disease Syndrome (IBDS) were noted. Our exposure definition for IBDS was based on Shimanuki et al.’s (1994) work on Parasitic Mite Syndrome (PMS)

Another term that one hears, here and there, is "snotty brood"

Maggi, M., et al. "The status of bee health and colony losses in Argentina." Honeybees: Foraging Behavior, Reproductive Biology and Diseases. Ed. Cameron Molley. Nova Publishing Group (2013): 212-234.

> The ectoparasitic mite V. destructor impairs both brood and adult bees causing a non-uniform disease pattern called varroosis or parasitic mite syndrome and including a specific form of brood damage termed “snotty brood” (Shimanuki et al., 1994)

You will note this reference to Shimanuki 1994 which refers to this publication:

Shimanuki, H., Calderone, N. W., & Knox, D. A. (1994) Parasitic mite syndrome: The symptoms. American Bee Journal 134: 827–828.

> The impact of the parasitic mites Acarapis woodi and Varroa jacobsoni has been devastating. In addition to reports of field observations, the Bee Research Laboratory has seen an increase in bee disease samples that we in the Laboratory have chosen to call the "parasitic mite syndrome." The entire colony, both adult bees and food are affected. Symptoms can occur at any time of the year, although we are seeing more samples from mid-summer into fall. It is important to note that not all the symptoms may be evident in any one colony at a given time. Parasitic mite syndrome is more likely to be associated with colonies that are infested with V. jacobsoni than A. woodi. Judging from the large numbers of affected individuals, the syndrome most likely is caused by a communicable agent. The purpose of this report is to heighten the awareness to this syndrome and to report our observations. It is our desire that this report will encourage others who have made similar observations, to share their knowledge so we can identify the possible causes.

In the authors’ opinion, parasitic mite syndrome is more Iikely to be associated with colonies that are infested with V. jacobsoni than A. woodi. Judging from the large numbers of affected individuals, the syndrome most likely is caused by a communicable agent. Bailey and Ball ( 1991) report that direct inoculation of either the acute bee paralysis virus or the Kashmir bee virus in adults or pupae can result in mortality. It is somewhat confusing that colonies with the parasitic mite syndrome benefit from the feeding of oxytetracycline or sugar syrup, both of which are not known to be effective against viruses. The effectiveness of fluvalinate impregnated plastic strips strongly suggest an association with V. jacobsoni. We do not believe that this syndrome results from the use of any acaricide. Until we are able to find a causative agent(s) for this condition, we would like to propose the name "parasitic mite syndrome." In the next publication we will report our attempts to isolate virus(es) and other microorganisms that may play a role in the parasitic mite syndrome.

This is the origin of the term "parasitic mite syndrome," but they make no mention of "snotty brood." They do mention the presence of larvae "molten to the bottom of the cell" -- which I suppose amounts to the same thing, without the more descriptive adjective. It is mentioned here:

Current State of Knowledge of Pathogens and Best Management Practices. Dr. Diana Cox-Foster, Pennsylvania State University, University Park, Pennsylvania; Dr. Jay Evans, USDA ARS, Beltsville, Maryland. 2012

> new species have been discovered using metagenomics, and new pathologies have been described, including melanization (chemical defense against invasion of internal tissues by pathogens) of bee organs and brood pathologies such as “snotty brood”


PLB

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