You are not starting a client list. You have one. The job is getting it across without retyping it or asking anyone to fill in a form.
Invite, do not import
You send an invite to a pet parent’s email. They open it, and they arrive already attached to you — your business, your prices, their pet. They are not signing up to a marketplace and then hunting for you in it.
Nudging the ones who have not got round to it
People are busy and an invite gets buried. You can send a reminder, paced so it stays a nudge rather than a pestering: one reminder per day, and three per invite. After that the invite stays open — they can still use it whenever they get to it.
Start smaller than you think
You do not have to move your whole book on day one. Most groomers start with the pet parents who book most often, run a few grooms through, and invite the rest once it is obviously working. Nothing about Clippie needs your book to be complete before it is useful.
What the pet parent sees when the invite arrives is in invited by your groomer.