Reading what you have just provided, I don't know if these two jobs are still in the backlog (with one in a killing status and the other in a running status for the last 3 week) and that person want you to get ride of it from the backlog with the help of the Database team. Or if this has already been resolved and is no longer in the backlog.
As mentioned, the word "Decommission" have varying meaning and from various other users/customers... sometime it mean to delete, de-activate, clean out of backlog, remove for x workflow etc... as that being said... to find out the intention when they told you to "Decommission" the job... I highly recommend talking to that person that told you & the your Application Team team... as we are not your organization nor that person that informed you to "decommission", to be able to tell you with 100% certainty that decommission mean = _________ in this particular scenario.
From my perspective I don't know if they just want remove the jobs from the backlog (as it been stuck there?) or if its not working correctly and want to delete or maybe to deactivate it. Or even just to remove it form the job... With what you have asked, the best we can do is GUESS that person intention, when they mention the word "Decommission".
Again, I recommend asking the person that inform you to "decommission" to clarify their intention.