As @vince says, the best option is to speak to the owners of the website and ask if they can set up an official channel to communicate this.
While there is nothing available on that layer to show when a change has been made, technically it will be possible to write a program to access the data programmatically and detect the changes yourself.
The legality of this is another matter. You could argue that you're merely accessing the same data which is visually available on the map, but in an automated format.
You can obtain the raw records of the Areas Scheduled for Spraying layer using a query to this URL:
This requests all records (
where 1=1) in JSON format (
f=json) for the fields specified in the
This won't tell you whether something has changed, but you could run this query in a script every 30 mins and compare the latest result with the previous result, and calculate the change manually (eg by examining the date, locname, work order and status fields).
Actually detecting the changes, and emailing you when they're found, is outside the scope of GIS Stack Exchange. But a competent programmer using something like Python could put this together reasonably easily.