Problem where path was laid

I wondered if anyone would be able to offer me any advice please.
I laid a new lawn last October and it has been doing very well, the only problem is at the side of the lawn there was a path about 4-5 metres long which i decided to take up and lay turf where the path was. The lawn tends to struggle along this strip where the path used to be and looks slighlty brown in places.
Is there anything i can do to try and improve the look of this strip. I have overseeded it and watered it regulalry when there hasnt been much rain but i just wondered if anyone has any tips?
Many thanks.

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