The offer, accessible on Bed Bath & Beyond's website, expires Thursday at midnight.
Bed Bath & Beyond will reimburse shoppers in the form of a gift card.
Shoppers won't get the full value of the Toys R Us cards, however.
The home goods company is offering to purchase the cards at a discount as Toys R Us winds down its US business by closing all its stores and shutting down its websites. In return, the company will pay shoppers in the form of a Bed Bath & Beyond gift card.
The offer, which is accessible on Bed Bath & Beyond's website, expires on Thursday at midnight.
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Shoppers who take advantage of the offer won't receive the full value of their Toys R Us gift cards, since Bed Bath & Beyond is buying them at a discount.
The company will reimburse shoppers for about 65% of the value of the cards. Bed Bath & Beyond will pay out $64.20 for a $100 Toys R Us gift card, for example.
But it's still a good deal for shoppers who are running out of ways to spend their Toys R Us gift cards, after Toys R Us abruptly shut down its websites last week.
The value of the gift cards at Toys R Us will expire within two weeks.
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