Someone knows the purpose of this undocumented oracle hint :
BYPASS_RECURSIVE_CHECK
Why to use it or not?
You should never use that hint. It's undocumented for a reason. If you were meant to use it, it would be documented.
As far as I'm aware, there are occasional cases where the optimizer generates plans differently when optimizing recursive SQL statements. This hint is intended to affect that. Realistically, unless you are a developer working for Oracle who is having a conversation with the optimizer group as to why some of your recursive SQL statements aren't generating the plans you would expect or you're a developer with an open SR with Oracle Support that is instructed to use this hint to work around an optimizer bug, you're almost certainly better off ignoring this and any other undocumented hints you come across.
If you really want more information, you can take a look at MOS ID 398605.1 which has links to a few related bugs.