There are a few main ways I can think of TACCP threats with packaging. The first is presumably there is some level of tamper evidence afforded by the lid. If that doesn't work you could have undetected contamination by an ideologically motivated attacker in the supply chain. Examples I've seen where tamper seals fail in this way is where the whole lid including a break off portion was not specified correctly meaning the whole thing could be taken off and replaced without damaging the tamper seal.
Secondly think about the incidents back in the 80s (you're probably too young) of attackers contaminating food by planting it back into supermarkets. That's where a lot of the tamper evidence came in. If someone had access to the unfilled packaging, through lack of security at your supplier site, they could then fill it with contaminated product, seal it themselves (depending on what kind of lid it is) and put it on shelf.
Then there could be their staff contaminating the food contact surfaces themselves if they were disgruntled employees. How have they considered that threat?
Lastly this is a packaging thing which may or may not apply in your case but on some packaging once, a disgruntled employee changed the date code to say "sh**" instead. Another in the artwork department made the cute cartoon characters on pack look like they were doing something sordid...
Funny but led to a withdrawal. OMG I didn't mean it that way... 