You can reset the drip campaign by going to the leads' profile tab, and scrolling down to their individual drip settings. Click 'Restart Drip' to change the Current Drip Day back to zero:

You may only reset drips a limited number of times. This counter may not be reset. It's important to not reset campaigns in batches or too many times, as you will hit your hard limit for sending mail in Gmail very quickly, and get your account shut down!

If your admin opted to send drips from our server, there is no limit on how many drips you can restart per day.  If the admin opted to send drips from GMail there is a limitation of restarting 10 drips per day.   Drips are reset one at a time, per contact.

Drip campaigns are always beginning on the day the lead was created, not the date the campaign was assigned, unless you use this reset feature.