I've got one strange problem (at least for me

. On short: an ERP with DB Oracle. One ERP session running time is too long and it also uses ~99% CPU.
History. Couple years ago our ERP/DB support did some things on DB (sth around statistics I suppose). And after that our "problem maker" session worked much better (from 1-2 hours to about 15-20 min).
A while after someone suggested to rename IDX1 (from main table of that session) to something else (IDX11). 'Maybe,' he said 'index is not created well and oracle will work by its brain and uses another index.' So be it. Trully, a running time went ~50% better.
Present. It happened some weeks ago that data had to be restored (around 300 tables, some of them empty). After that a running time of our nasty session was bad again (+5 hours!). And renaming an index did not help anymore. Is the problem a restore?
I know I write very messy question / problem, but maybe someone would say: hey, this is it!