Rose is right. For words and phrases like that, the end of "that" and "take" are not aspirated. This means that we don't complete the word with a breath, but move to the next word. So "take" may sound like "tay-kuh", with the K being exhaled. "Take" may also sounds more like "Tayg" (G like girl), because you don't breath out when you finish the word (essentially the tongue stops at the back of the throat). English speakers typically save that breathe for "this" or extend it into the word. This makes speech flow better.

Hello there, To pronounce the TH sound you bite have to bite your tongue when pronouncing the word. With time and practice I am sure that you'll be able to master this.

I would say /t/ is not heard in this combination. It would be fine for you to master the pronunciation of /th/ sound by saying tongue-twisters, for example: Whether the weather be fine Or whether the weather be not, Whether the weather be cold Or whether the weather be hot, We'll weather the weather Whatever the weather, Whether we like it or not. With time and practice, it gets much better, good luck!

I have similar problems with "R"s in German. If it helps: for "that thing", you almost don't say the "t" between the two words.