Bought this home a few years ago and had a new washer and dryer installed by Lowe's. It's an 1960s model. Turned the dryer on annd noticed the utility room was warm. Turns out the cats managed to pull the vent off the exhaust exit. While putting it back on I realized the metal flange was not covering the drywall allowing some exhaust back in the room. Admittedly I should have noticed this sooner as we have snaked the line twice before. Is this fire hazard? Minimal exhaust backs up but I'd rather be safe than sorry. Thanks.

Is there not any vent plumbing between the wall flange and the exit on the other side of the wall? There should be. That's not ok to use the wall cavity as your vent path.

Yeah, it's weird that that is coming back in. There should be a hard pipe going outside the house

To be clear, if there is, you could still get some warm air getting back in. If the hard pipe isn't sealed at the penetration, you could get some warm air returning into the house.

Y'all pretty much answered my question. I looked from the outside in and there is a metal tubing going through my wall connecting to the duct. Like I said, minimal air coming through that small gap in the Sheetrock. I've got to clean the duct out soon so I will pull it all apart and replace what needed when I do that. Thank you both!

while you're at it, replace that flexi duct with something rigid and smooth.