"I drink tea on Sundays."
I notice that both "我星期日喝茶。" and "星期天我喝茶。" word orders are accepted (please ignore the two different words for Sunday).
I'm curious...is there any difference in meaning or connotations between these? Sort of like in English we might say "On Wednesdays we wear pink." vs "We wear pink on wednesdays."
Like in English, saying "On Sundays..." places an emphasis on the day, often implying a contrast or comparison with the other days, whereas starting out "I drink tea..." doesn't have this emphasis.
With the way Chinese sentences are structured, any time qualifier/reference is usually put either at the start or directly after the subject and before the rest of the sentence. So 我星期天喝茶 and 星期天我喝茶 are both acceptable answers but yours is not. (At least that's the way I was taught and Duo seems to agree :) )
Word by word translations are never a good idea. Word order differs by language. What may seem a natural word order in one language may at best sound awkward in another (even if grammatically possible), at worst not be intelligible. In this case, the English translation asked for the neural English word order without emphasis, which happens to correspond to a different neutral word order in Chinese. Chinese and English are still to some extent similar in word order (SVO- languages) so it may have worked out for you some times in the past, but you will hit a wall at some point, so I suggest getting away from this literal approach.