Search for how to win repeat purchases from marketplace customers and you will get a wall of retention software, all of it assuming the one thing you do not have. The email address. The marketplace kept it, that is the deal you signed, and no flow builder can send to a contact that does not exist.
So the honest starting point is that you cannot retarget these people. You can only be findable by them, and make them want to look.
That reframes the whole problem, because being findable is a supply chain question long before it is a marketing one. The customer who loved the thing you sent will go looking for you using whatever words are physically in front of them, which means the box, the label, the care card and the item itself. If your brand name appears nowhere on any of them, the search she runs is the product description, and the result she lands on is your competitor’s listing on the same marketplace. You have paid to acquire a customer for somebody else.
Fix that first, inside whatever the platform’s rules allow, and fix it on the packaging rather than on a flyer nobody reads.
Second, make sure your brand name actually resolves. Search it yourself, from a logged-out browser, and see what comes back. If the marketplace listing outranks your own site, the buyer who types your name is being returned straight to the channel that will take another commission. That is a solvable problem and it is usually solvable in an afternoon.
Third, measure the thing everyone tells you is unmeasurable. You cannot see customer IDs, but you can export a year of marketplace orders and look for the same delivery name and postcode appearing more than once. It is rough and it undercounts, but it turns repeat purchase from a thing you assume into a number that moves, and a rough number you actually watch beats a precise one you never get.
None of this is as good as owning the list. It is not supposed to be. It is what is left after the platform has taken the part you wanted, and it is considerably more than nothing.
You do not have a retention problem on marketplaces. You have a findability problem, and it is mostly solved with a printer.
If this is the exact wall you are staring at, tell me what you are seeing: mail@sandeepkv.com, or message me on LinkedIn.