Having a min. offer - but not showing it - but still enforcing it, is dumb.
Anyone can figure it out and send you the min. offer anyways. I literally just tried it myself with a couple different domains; took me less than 10 seconds to figure out the min.
If they really want to hide it, they should let the buyer submit the offer then immediately send them an email saying 'the offer was automatically rejected because it was too low' and give them an opportunity to try again with a higher offer. In other words; instead of setting a 'min. offer', give the seller the option of automatically rejecting offers under $____.
Edit:
On second thought, even that can be easily circumnavigated...
My advice then is to just get over it. lol.
Show the min offer or don't set one at all, and deal with the consequences of whatever you choose. Because, setting a min. offer but not showing it is more likely to frustrate the buyer and encourage them to go in a different direction than it is to provoke a higher offer out of them. At least if they're able to submit the min. offer, a serious buyer will be engaged, and you can then negotiate up towards your desired price.
2 tips off the top of my head:
1. Set more realistic min. offers; if you set it to $100 but then get mad about recieveing offers of $150 or $200, that's your own fault. Set it to $500 or $1000 or w.e range it is that's closer to your desired price.
2. Use '9's; set your min. offer as $99 or $999 or $9999 etc. This makes it more clear to the buyer that the min offer is more of a range than an expected price.