The BankRec balance should synch up with the GL bank account balance only as of now or at the end of a previous month/period, because GL fiscal periods are not sensitive to a particular day but rather as of the end of the period.

Did the BankRec bank and GL previously have synched balances and then something changed? Or have they never been in synch? This is important. It may be that some transaction(s) was posted in BankRec but not yet retrieved and posted in GL. Or perhaps the BankRec bank balances was not set correctly in the first place.

Do you get the same balance in BankRec when printing the 'Bank Reconciliation' report as of the same date?

If you can determine what the correct bank balance should be and which location is wrong (BR or GL), then a solution would be easier to determine. It may be just a matter of posting the batches in GL. Or you may need to create a journal entry batch in either BR or GL to fix the balance (and if fixed in BR, delete the GL entry that this generates instead of posting).