They have no legal right to keep the warranty card. You bought the watch, it belongs to you. Challenge it if they try.
They know that they can move that watch if wanted to someone who will agree to those terms if you don't.
You know that.
@Regal started
London Fixed Gear and Single-Speed is a community of predominantly fixed gear and single-speed cyclists in and around London, UK.
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They have no legal right to keep the warranty card. You bought the watch, it belongs to you. Challenge it if they try.