So here’s the thing: Illyrio says that Jorah was anointed by the High Septon. However, Jorah says in ACOK Dany I that he got his knighthood for storming the breach at Pyke, and the WOIAF app confirms that Robert knighted him.
There’s a coujple Watsonian explanation: Jorah might have been anointed in a victory celebration later but didn’t convert, or Illyrio’s making shit up b/c he wants Dany to trust Jorah so that Jorah can be his man on the insdie once Dany leaves for Vaes Dothrak.
The Doylist explanation: early installment weirdness on GRRM’s part.