A paper discussing the autopsy methods and results of eight COVID-19 patients revealed that two of the patients had previously unknown papillary thyroid cancer. One had advanced papillary thyroid cancer with pulmonary metastasization and another had previously unknown papillary thyroid microcarcinoma of 3 mm diameter.

While one of the two (Patient 8) had SARS-CoV-2 RNA found in their thyroid, the other (Patient 5, with the microtumor) did not. 

I believe both instances are due to SARS-CoV-2 infection. One due to direct thyroid infection and the other due to an active infection of or reactivation of EBV. EBV is considered a significant cause of papillary thyroid cancer. Perhaps both factors are in play as EBV could have been active in both patients and the body may have cleared the virus in the other. 

A study from Wuhan University published 25 May found that EBV/SARS-CoV-2 coinfection was associated with fever and increased inflammation. EBV reactivation may associated with the severity of COVID-19.

Given that only 44,280 people in the USA are diagnosed with thyroid cancer in a given year, the odds of 25% of a population (however small) randomly having it are statistically improbable.