Downside of the strip beds

We love the quick setup, ease of use etc of our strip beds BUT it turns out the animals love to be at ease in them!  Crazy Lucy (cat) loves to lounge on the young seedlings and Jesse (Bassett/Bordercollie pup) thinks he should sit in the tomatoes to drink out of the little water dish I have in one.  They're only a foot tall, so apparently it's like an animal throne lol.  I'm hoping that me running them out will get the "don't get in there" message through.  Not holding my breath though - I've found that once they like a spot it's pretty hard to convince them that it isn't wonderful.