I would ask a different question... Ok I'd ask a whole heap of questions!
1. How do you know it's your packaging? Now that opens a whole can of worms... I've had metal detection "false rejects" which were later found not to be false. In fact in one site we're considering using it as an early warning system of something trending out of control. Just because on a physical inspection you didn't find anything doesn't mean it was false.
Metal detectors are really good at detecting metal but not necessarily at telling you what form it's in. For example, metal detectors can detect "metal dust" or swarf from wearing machinery (and do so before an x-ray sometimes if the total quantity in the pack is above the detection limit even if they're all very tiny pieces.)
So I'd be REALLY sure that it's definitely your packaging. What you could do for this is a natural experiment. For example, look at false rejects over time. Have they changed? If you have more than one line using different equipment, are the levels the same? Also it's good to sense check if you're getting any consumer complaints for metal? If this flags up any concerns at all, I'd be VERY wary in assuming it's just the film.
2. Why have you not changed your settings or equipment? If your packaging is setting off the detector then that's not a great test. So if you're absolutely sure it is the packaging, let's look at a few things:
a) You should be designing a test which minimises false rejections. It looks like you've not done so here. Could you decrease the sensitivity slightly while still being an effective test for the kind of machine damage you may get from time to time? This may seem counterintuitive but decreasing the sensitivity may increase the food safety. Right now, your staff will assume every activation is false. If you can really minimise false rejections, they're more likely to take a reject seriously.
b) There's other kit out there. Alternatives could include x-ray (expensive but effective) or if this is into a bag you can get throat metal detectors which detect just before the package is made and so is only checking what's going into the pack not the packaging. If you can't afford to change equipment now, can you plan capex for this for next year or the year after?
3. Why are you going back to the last good check? From your question, as I understand it, this is a false reject not a failure of a test pack to reject. Is that correct? If so, there is no need in UK standards at least to recheck since the last good check. That's if the test failed. A false reject should be rechecked individually and broken down until the contaminant is found and ideally shouldn't be put back into product flow (although some standards permit it if rechecked without detecting anything three times in three different orientations.)
4. Are you REALLY sure about the rest of the line set up? The reason I ask is I'm sure our British operators are no different to any others in that they are renowned fiddlers and tweakers! Even settings behind high level passwords end up with someone finding out, normally within a day (I am not kidding) and making a change to the programme. I really would rule this out. What if your "false rejects" were actually mistiming and rejecting the wrong pack?
5. Why are you living with this? I suppose that's been the whole point of my reply. But if I audited you it would alarm me from a cultural point of view. Because operators would almost always ignore rejects (and risk putting them back through without sufficient checking.) It also is an indicator that investment for food safety isn't priority...