First of all, recipients of your Haystack card do not need to have the Haystack app, sign up to Haystack or accept any T&Cs or privacy policy. Anyone can easily receive your Haystack card and save it to their contacts on any internet connected device.
If you're on a Haystack paid plan, you can also get analytics on what recipients do with your card (How many saved your card to their contacts, How many checked out your LinkedIn profile, etc).
For privacy reasons, we anonymize the data we collect and therefore, Haystack will never expose the identity of 'who saved your details' to their contacts - this is an illegal practice in most countries around the world.
This said, if a recipient chooses to send you their details (the system offers them a simple form to do so once receiving your card), Haystack will send you the contact details of the recipient and save it into your contacts.