If your new Fujifilm X-T1 carries a serial number lower than 41M07801, you are being advised to contact Fujifilm's customer service team (0844 553 2322 in the UK). This is to arrange for your camera to be inspected and, if necessary, adjusted to remedy a flare issue that some units from early in the production run are experiencing.
A manufacturing fault means that if the connector port cover happens to be open while images are being shot and strong sunlight is shining into the port at a certain angle, the light can be reflected within the camera body and be recorded on the images. These aberrant rays of light render as a flare effect for those photographers who've seen it. As the connector cover is usually closed and the light has to be at a particular angle, it's a relatively rare occurrence. Still, best to have it checked and, if necessary, repaired.
Fujifilm will carry out this service free of charge.