Changing auto.text = FALSE does work, but it does make your plot title bold, with no obvious way to unbold. A bit frustrating since I have to make these plots for multiple communities and keep them consistent, but I guess I'll be using auto.text = FALSE for all the communities to make all the titles bold.

test <- as.data.frame(airquality)
test$date <- NA
test$date <- paste(test$Month,"-",test$Day,"- 2024")
test$date <- mdy(test$date)
calendarPlot(test, 
             pollutant = "Ozone",
             month = 5,
             statistic = "mean", 
             annotate = "value",
             main = "'Delta' Junction Air Quality Index"
             auto.text = FALSE
)

Additionally I tried saving the title I desire as an object and then feeding it into the main = in calendarPlot() which still produced the delta symbol not the word delta.

title <- "Delta Junction Air Quality Index"
calendarPlot(test, 
             pollutant = "Ozone",
             month = 5,
             statistic = "mean", 
             annotate = "value",
             main = title)