You say "Makkah" when alone, but in a title it's "Makkatu-l-Mukarramah".
Why does the same letter sound like "h" sometimes and "t" other times? This is the rule of Waqf (Pause).
In the Middle of Speech
مَدِيْنَتُ الرَّسُولِ
Madinatu-r-Rasool
The City of the Messenger
ة sounds like "tu" — the Ta' is fully pronounced, connecting to the next word.
At the End (Pause / Waqf)
مَدِيْنَه
Madinah
A city (said alone, with stop)
ة sounds like "h" — when you pause/stop speaking at this word, the Ta' softens to a "h" sound.