I cut it out too. With one of my previous pregnancies I had a mw appt fairly early in the morning. I stopped by mc'ds and had an iced coffee. When I got to my appt we did the usual routine and then listened to the heart beat. My midwife became alarmed as did i, the babies heartrate was so incredibly high. She asked me everything I ate and drank that day...i told her..but forgot the coffee. She asked are you sure you had no caffine today? Oppps. I told her and she informed me I had given my baby a caffine high.
I had never felt like such a terrible mother before in my life. But after hearing how high that poor babys heart was pounding to keep up with the caffine...it broke my heart...I haven't touched caffine during pregnancy since.
Its different when you can't see the effect your choices make on your baby, and when you can. Your baby's heart works overtime when you have caffine.