Learn English – Odd pronunciation of adjectives ending in -ed

The National Association of Realtors, who own the trademark on the word Realtor, have severe paranoia about their trademark—I would call it “trademark anxiety”. They always put that registered trademark symbol next to the word "Realtor". Like, even if it appears 100 times on a page, every instance has it with the ®. And it's always in all caps. Look at Realtor.com, or as they call it, "REALTOR.com".

In any case, nobody actually says "real-TORE" like they do in the ads. It's just another way for them to assert their ownership over the trademark, by attempting to control how it is pronounced. This is similar to stunts pulled by the people at the Lego company, who put up a page once telling people not to use the word "Legos". I wrote an answer about this before.

The standard pronunciation of a word such as months is /mʌnθs/, as Barrie indicated. Here the /θ/ symbol indicates the th sound as found at the beginning of thin or the end of month.

However, you've correctly noticed that the word months is not often pronounced that way, and many people do indeed say something like /mʌnts/, using /t/ rather than /θ/ for the second-to-last sound. There are two things going on here:

1. The sequence of sounds /θs/ is very difficult to say, and it is very often reduced to simple /s/, especially in rapid speech.
2. The sequence /ns/ is also somewhat difficult to say, as the transition from nasal /n/ to voiceless spirant /s/ is problematic. The letter s following n is usually pronounced as /z/; where we have an actual /s/ sound following /n/, a /t/ often gets inserted in pronunciation. For example, the word chance often sounds just like the word chants. This intrusive /t/ is called an epenthetic consonant.

So I believe that what's really going on here is a two-stage process:

θs > s    (deletion)
ns > nts  (epenthesis)

Both halves of this process can be frequently observed in a variety of words, while the direct change from /θ/ > /t/ is not widely attested.

This does not mean that the pronunciation /mʌnts/ is incorrect. It is, in fact, one of the most common spoken forms of this word, and it occurs because of normal, unobjectionable phonological processes in spoken English. You absolutely should not feel like there's anything wrong with months as munts.

Note that in any case it's very misleading to talk about "dropping the h". There is no /h/ sound anywhere in either pronunciation. The spelling convention th is just an orthographic convenience, and the th sound /θ/ has nothing to do with /h/.