In photo 1 in the sequence above it appears that the the gap between the free edge of the door and door frame is covered by a moulding of some sort. If so forget trying to "pick the lock" with a flexible piece of plastic. The normal technique is to slide the piece of plastic between the door frame and door above (or below) the lock tenon then shuggle it to the the tenon then shuggle it some more in the hope the card will get around the end of the tenon; this is made easier if there is an engaged handle one can shuggle up and down and/or the door is a "rattling good fit". With a moulding covering the gap it will be next to impossible as one will be trying to insinuate the plastic around a right angle bend. This likely will cause the plastic to break or take up a permanent set, also the tenon appears to be cunningly designed to eliminate the possibility of using a piece of plastic. Remember the professional only likes easy targets.
Anyone on here an experienced in B & E ?
I had to look up what shuggling a tenon meant. ;) Yes, I see the difficulty of getting anything as flimsy as a sawn-off credit card around the moulding and into the tenony bit.
I have seen someone pick a similar lock when a neighbour got locked out, but I couldn't get close enough to see how it was done and, unfortunately, I'm not sure I could actually ask without getting strange looks.
Otherwise, I have seen emergency locksmiths with implements that looked as if they belonged to a dentist.
Even so, I
still don't understand the credit-card demo as the only way to pick a lock. Nor why a screw would have been in the way.