How might Bitcoin change the remittance industry, if at all?

Bitcoin will not change remittance, bitcoin itself is remittance. Remittance is just nomenclature for cross-border money transfer and that too, specifically tied for migrant workers remitting money.

It will be a while before Bitcoin is widely adopted as a mechanism for conducting remittance transactions. I will cite a couple of reasons for this:

• Majority of the migrant remittances are done by folks with little or no education. These are predominantly blue collar workers, and for them to widely adopt a crypto currency in its native form, is a hard sell to say the least.
• The beneficiary to whom they are remitting the money, share the same demographics. If you are expecting an impoverished family in Bangladesh or India to embrace Bitcoins as inward remittance (in its current form), that is most likely not going to happen.
• The current state of Bitcoin ecosystem makes it very difficult to buy/sell bitcoins on a global level, horizontally speaking. Its not as simple as technologist or enthusiast would like you to believe vis-a-vis the current traditional remitting channels.
• Volatility in price with respect to your Buy/Sell fiat currencies.
• Cashing out of Bitcoins in Beneficiary countries (not widely available in remote areas, even urban areas)
• Licensing. Sooner or later, it will be licensed.