Helena does indeed confess to Hermia that she let it slip to Demetrius that Helena and Lysander planned to cross the woods into his aunt's city to elope. Helena makes this confession at the most intense point of the fight that breaks out between the four characters in the woods. The fight occurs because, not only does Helena feel scorned by both Lysander and Demetrius, she feels that her dearest childhood friend Hermia is in on the joke as well. When Hermia gets angry at Helena for stealing Lysander from her, calling her a "thief of love!," Helena responds back with angry words, even making a joke referring to Hermia's short stature by calling Hermia a "puppet" (III.ii.292, 298). The heated words continue until Helena begs Hermia not to be angry with her, declaring that she has always loved Hermia and never wronged her, except for the moment that she told Demetrius of her and Lysander's plans to elope, as we see in her lines:
I evermore did love you, Hermia,
Did ever keep your counsels, never wrong'd you;
Save that, in love unto Demetrius,
I told him of your stealth unto this wood. (III.ii.318-321).
Hence, we see that Hermia does indeed find out that Helena betrayed Hermia's and Lysander's elopement plans to Demetrius due to Helena's own confession.