From the Episcopal Diocese of El Camino Real, we have this explanation from Michael Gloucester:

Under the Overseas and Other Clergy (Ministry and Ordination) Measure of 1967, which in my view needs urgent revision, but which is still in force and which must therefore be respected, clergy from abroad (Anglican or otherwise) need the permission of the Archbishop to officiate here. My understanding is that over the years, this rule has not been tightly followed in the case of those visiting partner dioceses for short periods of time, but only for those seeking to take up a ministerial post here. However, with all the present tensions in the Communion and with some people prepared to use legal processes to challenge bishops and others who do not follow the letter of the law, the Archbishop’s office has thought it best to ensure that the rule is strictly adhered to. Thus I have sought and obtained permission for Bishop Mary for preside at the Eucharist in Gloucester Cathedral.

(....)

The Measure makes no reference to what the bishop wears. As it happens, the simple weekday Eucharist at which Bishop Mary will preside is not one when either she or I would expect her to wear a mitre. However in the Cathedral on Sunday, when she stood at my side when I presided at the Eucharist and again when she preached at a Partnership Service later in the day, she did, like me and Bishop Gerard, wear her mitre.

Read the whole and accompanying letter from the Bishop of El Camino Real here.