I do the see but no touch integration for at least 2 weeks but that is just me. The only pecking that happens is with integrating new roosters, sometimes I do 3 weeks of see but no touch for them and then everything goes well. When introducing new pullets, I don't have the pecking issue because...
I also do this but I don't have experience with having the chicken with the flock for a month already and then trying to reacclimate into the flock. Not sure if it would help or not.
Possibly, the partner may rank above her in the pecking order in which she still would be on the bottom or the new one will replace her for the bottom of the pecking order.
How many chickens do you have?
With a partner they may not still except her the way you want them to.
There will always be a chicken on the bottom of the pecking order.
Having extra feeders and waterers will help.
Did you integrate her into the flock or just put her into the flock? How old is she now?