泰 is not in Kanjidamage (yet, probably never, banned as not frequently used). So how are we supposed to find Thai food in Taiwan? Oh right, it may say so in English already.
泰國專賣店 Tàiguó zhuānmài diàn
The contracted brush shape looks a lot like other, similarly contracted characters. I'm thinking of 奏 and 奉. In both of them two hands offering some object were contracted to two simple strokes, while the different objects (and 大 in 泰) all became indistinguishable (a kind of 大 with two extra strokes).
In Japanese the word for Thailand is mostly written タイ国 (or タイ王国, the Kingdom of Thailand), but I'm certain 泰国 is also still around (Chinese is of course either 泰國 or 泰国).
安泰 antai is a priority word in Edict, and seems to have no homophones (no words that sound the same). 泰然 seems still to be in use as well, especially as 泰然として taizen to shite. 泰平 is the same as 太平. 泰成 taisei seems an old word for the West (not used really).
From the Tanaka Corpus:
So how to remember a character that means Thailand, peaceful or calm, and is written with 大 great with two extra strokes and a kind of 水 water? Try this: A Thai massage makes you feel peaceful and calm: which is just 大 great, involves two 二 hands and a shower (water 水). Or make your own mnemonic.