Sometimes. Support can reverse a recent recycle as a whole, as long as you still have all the currency (Threads, Bubbles, or a Pal currency such as Fluff) that recycle gave you. You can't undo it yourself in the app.
How does a reversal work?
The whole batch comes back. Each time you confirm a recycle is one batch. A reversal returns every item in that batch, never just one item from it.
The currency goes back out. The exact currency you received for that batch are taken back from your balance at the same time.
You need enough currency. If you've already spent some of what that recycle gave you, the reversal can't be done. Partial reversals aren't possible.
Time limit. Reversals are only available for recent recycles, so ask as soon as you notice.
Restart afterward. Once Support processes it, close and reopen Highrise and the items appear in your inventory.
How do I ask for a reversal?
Contact Support as soon as you notice, and include:
Your username.
Roughly when you recycled, with the date and time if you can.
What you recycled, or at least the item you want back.
Don't spend the currency from that recycle while you wait. Support will confirm which batch you mean and what will be deducted before going ahead.
Can Support return one item without the rest?
No. Reversals restore the entire batch. If you recycled many items at once, you'll get all of them back and lose all the currency from that batch. Support won’t be able to reverse the batch when the currency is insufficient, so make sure that you have enough currency left to cover the reversal.
How do I avoid this next time?
Check the summary before you hold the recycle button, and unselect anything you want to keep. Shortcuts like "select duplicates" can pick more than you expect. See How does Recycling work?