요 sounds much different, with a more narrow sound, closer to the "oo" sound than 여 is.
The reason you might here a "t" is because the j sound in Korean is pronounced differently, more towards the front of your mouth, if that makes sense. This sound is very common in East and Southeast asian languages.
If anything, the 아 of 자 is pronounced wrong.
Native pronunciation of 여자: https://forvo.com/word/ko/%EC%97%AC%EC%9E%90/#ko
Native pronunciation of the 요 sound: https://forvo.com/word/ko/%EC%9A%94/#ko
You'll notice that 여 is more open sounding. It's almost pronounced like a deep "yaw"
Wait. I always learned from watching native Koreans speak that 여차 was girl. How is it that the translation is now woman? Can it be both? I typed girl in when it asked me to translate the phrase, and it said I was incorrect. However, native speakers use 여차 as girl. Can someone explain?