I'll watch this later, I have some stuff to do but my theory goes like this:
Quainthe was painting some person's back during her conversation with Jorah and she said something like "he is going to Old Valyria, he needs protection". Jorah got his greyscale in Old Valyria. In the same conversation she asked him "Will you betreay her (Daenerys) again".
In the last episode, Daenerys finally forgave him, but told him to look for a cure for the greyscale.
Jorah contacted greyscale while he was taking Tyrion to Daenerys, through Old Valyria, hoping that would placate her.
Tyrion just made a deal with the slaveholding cities, in Daenerys' absence to abolish gradually slavery in 7 years.
Quainthe is in Qarth, one of the slaveholding cities in Slavers' Bay. (it is, right?)
I think this will be a plotline in the second half of this season.