See link for information about the Rewards Card
If you look at this link
and click on "Broadband" in the Important Information section and scroll down to "Reward Card" you will see information about claiming the card.
You must claim your BT Reward Card once your broadband is installed and you have 3 months from this date to claim. Claim your reward by visiting BT Reward Card and logging in with your BT ID. You must activate the card within 3 months of receipt. Following a successful claim, your card will be sent to the broadband installation address. Offer, BT Reward Card & BT terms apply. The BT Reward Card is issued by Blackhawk Network (UK) Ltd, an Electronic Money Institution authorised in the UK by the FCA with Firm Reference number 900023; pursuant to license from Mastercard International. Mastercard® is a registered trademark of Mastercard International Inc. Blackhawk Network (UK) Ltd’s company registration number is 05802971 and its registered office is at 40 Bernard Street, London, WC1N 1LE.
The following page also states in the FAQs that there is an expiry date of the card
You must claim your BT Reward Card once your broadband is installed and you have 3 months from this date to claim. After 3 months your claim will expire and you will no longer be able to claim. (If your order was placed before the 1st JULY 2016, then the 6 month claim period still applies).
It does tell you under the BT Reward Card User Terms and Conditions that you have to claim it, for your order to be placed and to join BT you have to tick the box stating you have read and agree to the terms, along with the terms it also states it in the frequently asked questions.