Intent surely does matter. Both the person making the 'offensive' joke and the person being 'offended' need to be understanding of each other.
Also, consider, the more 'offended' we are by things that are not meant to be offensive, the less likely we are to have companies and their PR interact with us in the way that this twitter account does.
If they find that unintended mistakes like this can cause negative impressions, they will likely go back to interacting with bland, vague corporate-speak. I'd rather give people the benefit of the doubt and consider their intent, especially on one-off mistakes like this, rather than throwing around labels at them like transphobic. This of course would be entirely different if I thought their intent was in fact to be offensive to our trans. brothers and sisters.
Another way to think about it is, if someone accidentally steps on my foot and hurts me, I probably won't care too much. I would appreciate an acknowledgement that it was an accident, but I wouldn't necessarily need it. On the other hand if someone did this on purpose, it would be a different story. Intent always matters.