Check what version of Excel folks are on. Just ask your colleagues straight up what they're using. Ideally, everyone sticks with Excel 365, or at least something from 2016 and up, you know, for the best shot at things working smooth together without glitches.
Embed those images right into the file, basically. Don't just link to them from somewhere else, because that can cause all sorts of headaches. Go to Insert, then Pictures, and drop it in there. Make sure it's actually embedded, not hanging out as a link.
Switch your images over to formats that play nice. Save them as PNG or JPEG first, before you bother inserting. That way, compatibility issues drop way down.
Look out for any formulas tied to those images. If they're getting generated on the fly or linked through some formula magic, double-check that it runs okay across versions. Or, you know, just turn them into plain static images to keep it simple.
If seeing the file right is the big deal and nobody needs to tweak it much, send it out as a PDF. Or flatten the pictures into a static copy. That sidesteps a ton of version drama.
Test it out on another setup. Grab a machine running the exact same Excel version as your team, open the file there, and see if the image mess shows up again.