I think that they are refering to your consent being given to another third party (not Sears) in the sentence “we receive your name, surname and email address from our partners”.
In other words I think they refer to a triangular relationship:
- you opt in company A, company A has something in their TOC that says “we can share your data with third party”.
- Criteo has a relationship with both company A and B.
- you browse company B, company B asks Criteo if any of their partners (A) has you opted in with the “allow 3rd party information sharing” clause. Criteo requests your info to A and gives it to B
That’s my best guess, so technically it would be legal even in stricter countries like France.