Obviously, as you've realised, your Manfrotto plate is not compatible with the Peak Design Capture clip. I think you'll probably be out of luck trying to find a backpack clip that accepts a Manfrotto plate directly. Your best bet is to use a plate that you know is compatible with the Capture clip, and which is also compatible with your Manfrotto tripod – there are options, which I'll get to below.
But first, just a bit of background. Tripod plates used to be, by and large, proprietary to the tripod manufacturer. At some point, the large-format camera maker 'Arca Swiss' introduced a well-designed system, which caught on with other manufacturers, and has now become something of a standard. Plates with this design are called "Arca-type", "Arca-compatible", "Arca-Swiss", "Arca-Swiss-compatible", etc, etc. (Not to be confused with another tripod company called 'Acratech'.) Manfrotto, however, continued with their own quick release systems, and didn't switch to the Arca system across the board like other manufacturers did. The most commonly-encountered Manfrotto system is probably their RC2 "Rapid Connect System", but there are others.
So if you find yourself with a Manfrotto tripod/head/plate, which you'd rather was compatible with the Arca system, then there are a couple of options – the easiest being to buy a plate that has dual compatibility with both the Arca system and with Manfrotto's system. Assuming your tripod head uses the RC2 system, Manfrotto itself offers the '200PL-PRO Plate', which is a bit of a novelty in the Manfrotto line-up in being compatible with both the RC2 system and the Arca system. I'm not sure this guarantees compatibility specifically with Peak Design's Capture clip though, and so if you want to use the plate with the Capture clip, I'd say it would be safest to stick to Peak Design's own 'Dual Plate', which is manufactured exactly for this purpose, i.e. compatibility with Peak Design's products as well as the Manfrotto RC2 system.
(Edit: Since writing the above, I've been able to try the Manfrotto 200PL-PRO Plate with Peak Design's Capture clip (v3), and I can confirm that the Manfrotto plate is not compatible with the Capture clip.)
There is another solution which might work. Manfrotto is of course aware that Arca-type plates dominate the market, and they've made available something called the 'Top Lock Travel Quick Release Adaptor', which is a user-replaceable part for certain Manfrotto tripod heads, changing them from the Manfrotto system to the Arca system. This would allow you to get the Peak Design Capture clip and Arca-type plate, and use the Arca-type plate directly with your newly-updated Manfrotto head. Buying the Peak Design Dual Plate is probably the easier/cheaper option though.