You only signed up with this store for the purpose of getting this free gift, and as the one who signed up does not celebrate his birthday or take it as a recurring day of celebration, then he is like one to whom a non-Muslim gives a gift on the day of his own celebration. It is a gift that is given on that occasion, in accordance with the system set up by the store, like a type of business promotion, and the store has nothing to do with setting up any celebration or taking that day as a recurring celebration or otherwise.
It was narrated that Muhammad ibn Sirin said: Someone brought a gift to `Ali on the occasion of Nowruz, and he said: What is this? They said: O Amir al-Mu’minin, it is the day of Nowruz. He said: Then make every day Fayruz! Abu Usamah said: He did not want to say the word Nowruz. Narrated by al-Bayhaqi in As-Sunan al-Kubra, 18865.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: As for accepting gifts from them on the day of their festivals, we narrated above from `Ali ibn Abi Talib (may Allah be pleased with him) that a gift was brought to him on the occasion of Nowruz and he accepted it…
All of this indicates that the fact that this day is a recurring celebration does not mean that we disallow accepting their gifts. In fact, the same ruling applies whether the gift is given on the day of their festival or otherwise, because that is not helping them in observing the rituals of their disbelief.
End quote from Iqtida’ as-Sirat al-Mustaqim, 2/52.
Similar to this is the issue of benefitting from sales and discounts that are offered around the time of Christmas and innovated festivals. The scholars have stated that it is permissible to benefit from that. See the answers to questions no. 145676 and 326165.
In the situation mentioned by the questioner, there is no celebration or helping others in their celebration, so it is permissible to make use of the free voucher, because the matter is flexible and lenient.
And Allah knows best.
