What change does Raina notice in Bluntschli's appearance when she meets him for the second time?

When Raina first meets Bluntschli, he looks terrible, and presents a striking visual contrast with Sergius's heroic appearance in the portrait. The stage directions tell us he is unwashed and unkempt, and  

"…in a deplorable plight, bespattered with mud and blood and snow, his belt and the strap of his revolver-case keeping together the torn ruins of the blue tunic of a Servian artillery officer."

Furthermore, his nerves are on edge. He...

When Raina first meets Bluntschli, he looks terrible, and presents a striking visual contrast with Sergius's heroic appearance in the portrait. The stage directions tell us he is unwashed and unkempt, and  

"…in a deplorable plight, bespattered with mud and blood and snow, his belt and the strap of his revolver-case keeping together the torn ruins of the blue tunic of a Servian artillery officer."

Furthermore, his nerves are on edge. He is starving and hasn't sleep for 48 hours. He is running from soldiers who intend to kill him. So this contributes to the visual impression he makes on Raina, and it isn't one that she would expect from a man worthy of her romantic interest.

Once she gets over her initial shock and distaste, she begins to show protective feelings towards him. She overcomes her prejudices, and when he tells her he is too dirty to take her hand, she even grants that he has the manners of a gentleman. At the end of the scene, when she finds him sleeping, she tells her mother to leave him alone:

Don't, mamma: the poor darling is worn out. Let him sleep.

So she has taken stock of his wretched appearance, and been touched by his vulnerabilities.

When Raina next sees Bluntschli, he is, according to the stage directions, "clean, well brushed, smartly uniformed, and out of trouble." She asks him about it, and he replies:

RAINA: You look ever so much nicer than when we last met. [He looks up, surprised]. What have you done to yourself?

BLUNTSCHLI. Washed; brushed; good night's sleep and breakfast. That's all.

Bluntschli is guilty of minimizing the crucial emotional differences -- what the stage directions called being "out of trouble." He is no longer under extreme stress, no longer running from death, no longer in hiding. He has freely chosen to come to this place, and for a romantic reason. As we learn later, he did so because he wanted to see Raina again. His changed emotional state and mood will have doubtless influenced his looks.