When the event launched, a countdown number of days to the weekly reset was displayed, but did not show an exact time. Now that we are within 24 hours, an exact time early tomorrow is displayed:
If you're interested in a currently sold-out item, you might want to log in as quickly as possible after this time to claim it.

You can view the timer in the bottom left corner of the prize shop.
At the time of writing, only five (shown below) of the nine items available have sold out this week, and so this restock is only relevant to those, though of course more may sell out later today. However, if there is an available item you are interested in, it might be a good time to grab it now to avoid being boxed out during a later week of the event!
We won't know the exact mechanics of the restock process until it happens, but based on messaging from TNT and in the app, it seems it will be the same prizes at the same prices each week, just with the quantity available reset. It also seems that once you have claimed a prize, you will not be able to claim it again in future weeks.