Here are my thoughts as an American English speaker; I don't have references for this so some of it may be wrong.
The pronunciation that sounds most natural to me is [mɛɾɚ], with /h/ omitted and the /t/ flapped and voiced.
I would not be surprised to hear [mɛʔt̚hɚ] in slower or more deliberate speech. By [ʔt̚], I mean to indicate an unreleased voiceless stop with some degree of pre-glottalization/glottal reinforcement. In fact, even complete or near-complete replacement of the [t] with a glottal stop doesn't seem too unlikely to me in this context.
I would definitely advise against using [tʰ]. There is no general principle that sequences of plosive + /h/ turn into aspirated plosives in English, so [tʰ] would just be heard as a realization of /t/, but in this context (the end of a word) aspiration of voiceless stops is not usual in most accents and would sound strangely emphatic to me. Also, if someone were to use such a pronunciation, I would expect the /h/ to be retained also: [mɛtʰ.hɚ] sounds much more natural (although, as I said, abnormally emphasized) than [mɛtʰɚ].
I don't know enough phonetics to know if [ɾh] is used at all. I don't see any point in aiming for it because I'm sure omitting the /h/ is much more common, and any pronunciation that includes the /h/ will likely separate the two words to a sufficient degree to make flapping unlikely.