If someone is remiss, they are careless about doing things which ought to be done. I would be remiss if I did not do something about it. careless because you did not do something that you ought to have done = negligent remiss in (past participle of remittere )
Not energetic or exact in duty or business; not careful or prompt in fulfilling engagements; negligent; careless; tardy; behindhand; lagging; slack; hence, lacking earnestness or activity; languid; slow