Confinement only checks the STR restriction when it's played. So once a character is targeted by Confinement, boosting its strength afterwards (with Widow's Wail for example) does not counteract Confinement because the lasting effect isn't conditional (if it were, it would read "Until the end of the phase, while that character's STR is 4 or lower, it loses ...").
- Icons are re-calculated each time a new modifier is applied. For example, if a Night's Watch character has a military icon to begin with, then loses a military icon from Confinement, he has 0 military icons (1-1=0). If that same character then gains a military icon from Ser Alliser Thorne, he has 1 military icon again (1-1+1=1).