So they have a 14 day return policy, after 30 days you want to return it, they won't let you and you want to know if they have the right to refuse replacement?
Yes they do, even if you had the original box. You are outside the return period. Now it is up to Samsung to repair or replace under warranty.
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Samsung Galaxy S4:
Rooted de-bloated Stock 4.2.2
Samsung Galaxy Note 10.1 2014:
D1 -> POS ThunderBolt -> Bionic -> RAZR MAXX -> Samsung Galaxy S4