bdc/bdel_auth_check is a SAP Parameter attribute which is used to control batch-input: check authorisation for activity DELE when delete TA information. This is available within R/3 SAP systems depending on the version and release level.
Below is the standard documentation available and a few details of the attributes values .
You can use this parameter to specify whether the authorization for
authorization object S_BDC_MONI for the activity (BDCAKTI) with the
value 'DELE' (delete sessions) is to be checked when deleting a
transaction from a batch input session.
FALSE No additional authorization check is performed. TRUE Transactions can only be deleted if the authorization for deleting the session exists.
See SAP Parameter Documentation for full SAP documentation for this profile parameter.