Ok keep it (presiously).
Normally, the "objective" is completed when you loot one thing in the inventory of the body (whatever the one).
So for test, reload the save, look if there no other "dudes" nearby. On you first screenshot, go down the stairs on the left, then at the end of the alley on the right (a little further) there might be more Tyger Claws. If there are, kill them first. Then kill the four in the assault in progress. And finally loot the body.
If the objective is not completed with the first item that you pick up, I'm afraid you have to wait a patch/hotfix. You can/must obviously report it to CDPR Support if it's not already done (the best way to see bugs/problems fixed).
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The most important, if you continue to play, do it from the save before (before killing the Tygers and loot the body).