Every gift you've reserved on Wishpicks is in Wishes → For others, grouped by list, and Home shows them too, in the section headed Coming up or To do.
Steps
On a phone:
On someone's list? Tap the Wishpicks logo at the top first.
Tap Wishes in the bar at the bottom, then For others.
Tap a gift to open it, with its store button and Cancel reservation.
On a computer:
On someone's list? Click the Wishpicks logo first.
Click the bookmark icon (Wishes) in the rail on the left, then For others.
Click a gift to open it.
Each group shows the owner's name and the list; tap it to open that list. The ⋮ next to a gift has Add to my wishlist, Cancel reservation and Report. Every list you've opened is on Home too, even if you didn't reserve on it: in that same section if its date is ahead, otherwise under Lists you've opened.
Seeing "Gifts for other people, in one place" instead? Nothing's reserved yet on this account, or in this browser if you're not signed in.
I reserved without an account. Where is it?
Only in the browser you reserved in, which is also the only place you can change or cancel it. That's what the Reserved window meant by "You can only change this reservation on this device". Open Wishpicks there to find it. Can't get back to that browser? The gift still shows as Reserved to everyone else, so if you're still buying it, you're covered. If you won't be, ask the list's owner to free it up: "How do reservations work?" shows them how.
To keep your reservations for good, sign in there: they move to your account and show up on any device. "Do I need an account?" has the steps. No account yet? See "How do I sign up or sign in?". Recovery links and backup emails cover lists, not reservations.
I signed up, but my reservations aren't there. Why?
You signed up in a different browser or on a different device. Signed up with an email link? Your mail app may have opened it in its own browser. Reservations made without an account follow the browser, not your email address. Open Wishpicks in the browser you reserved in and sign in there with the same account, and they'll move over: "Do I need an account?" has the steps.
Why did my reservation disappear?
The owner deleted the wish or list or cancelled your reservation, or you reserved without an account and that browser lost access to it.
Cleared cookies or a long break can do that. The wish still shows as Reserved to everyone else, so you can still buy it. If you won't, ask the owner to free it up.
Tips
See Fulfilled on a gift you haven't bought yet? The owner already has it, so check with them before you order.
A private window forgets you when it closes, so sign in before reserving in one.
Links tapped in a chat or social app often open in that app's own browser, which counts as a separate one, so open lists in your usual browser.