I'm back. After reading through my Win32API books, here is your problem. Whether you are creating a dialog box or an input box or a message box or new full-blown data entry form, you are always creating a child window for this form-like object. You HAVE to create a child window because under the Windows operating system, any code or activities associated with the window's content can get CPU time ONLY if they are represented by a child process of Access associated with the window. It is basically a CPU resource scheduling requirement. Creating a child window means that you have to abide by the WINDOWS requirements for that child. (One case where you CAN'T evade paying child support!)
There are certain features that are created in a child window. If you were to create the window yourself through a Win32API call to CreateWindowEx, you could specify that it had a thin border and no features in the title bar (and thus could also specify "no title bar" if you wanted.) I check for this next fact carefully: There does not appear to be a function to MODIFY the features displayed and extant in a newly created window. You have to create the window to initially have (or not have) the features that you want. Once it is created, it has the features it has (and lacks the features it doesn't have) for the lifetime of the window.
However, you aren't the one creating the window. Access is doing that based on some internal routine that we cannot see. There is no direct interface to what Access actually uses. Therefore, from an Access app, the only way to customize your message box is to custom-build it using only WinAPI calls. Is it doable? Yes. Is it easy? Not really. And while I understand it, I wouldn't want to have to do it. If you are not an experienced Windows app programmer, this might not be in your wheelhouse.
REFERENCE: Win32 Programmer's Reference, Vol 1., Microsoft Press, 1993. Chapter 1, Window Management. 1.1.5.4, Window Borders; 1.1.5.5, Nonclient-Area Components.