A number of websites and forums posts have talked about the differences. On that I spot is the locking screw shape

(picture from a thread here
https://shipsofscale.com/sosforums/threads/mitutoyo-calipers-buying-the-real-deal.7837/
The real ones have a lower profile screw (bottom set of calipers). Typically the LCDs are wrong in some detailed way. Also, they typically ship with alkaline vs sliver-oxide batteries. Sometimes the spare battery packaging will claim to be SO even when the battery itself says otherwise.
The sad thing is often the fakes are decent calipers and probably better than the HF stuff. If the machining was as poor as the last HF calipers I used no one would confuse them.
I've heard that ebay will not make you return a fake item but will force a refund to you. I've been tempted to buy some fake Mitutoyos just so I can get a refund because they are fake. It hurts the seller of fake goods and I would get a free pair of calipers. I've never done this because I've been worried that ebay wouldn't believe me when I say the tool is fake. Given I have more calipers than I need, not worth the trouble.
Incidentally, I haven't seen fakes of the older, smaller LCD Mitutoyos. If you can find them, some ST Industries branded calipers are actually older Mitutoyos. Mine are the "CD-6 C" models that have the power and abs buttons on the side vs front face of the electronics housing. Very cheap used since they aren't a "good brand".