I understood there was a notify congress 30 day in advance provision, but as you suggest it’s not in the section you quoted...
My apologies for not providing fully up to date material. I didn't check the previous link and assumed it at least had an update in notes or something. There is a 30 day before removal provision, signed into law in October 2008. Pub. Law 110-409 - Inspector General Reform Act of 2008
If an Inspector General is removed from office or is transferred to another position or location within an establishment, the President shall communicate in writing the reasons for any such removal or transfer to both Houses of Congress, not later than 30 days before the removal or transfer. Nothing in this subsection shall prohibit a personnel action otherwise authorized by law, other than transfer or removal.
In my opinion, there isn't any "meat" in the 30 day notice provision. See no prohibition on 30 day suspension, which is not transfer or removal. A typical law, looks good, but is INTENTIONALLY superficial or hollow. Any "meat" in Walpin's removal has to do with the reasons. See Nixon's Saturday Night Massacre, etc.