Hello Andrew
Sorry for the slow reply … lots going on here. Much work has been done on optimising feeds to illuminate a dish as efficiently as possible reducing spill over which on receive means the feed sees ground raising the system noise temperature and reducing the systems sensitivity. The one you have is a Dual Mode type which works very well for dishes with an f/D of around .45 which is a common format for dishes . A good place to start is the W1GHZ antenna handbook. https://www.w1ghz.org/antbook/conf/high_efficiency_prime_feeds.pdf and https://www.w1ghz.org/antbook/chap6-3.pdf.
You can find details of other types of feed in various chapters of the ( on-line ) book. There are simpler ones to make but depending on the f/D the dual-mode feed is technically amongst the best.
All the best