What is the point of view used in "A Worn Path" by Eudora Welty?

The point of view used in Welty's "A Worn Path" is third-person narrator/ limited omniscient. With regard to the character of Phoenix, the point of view is omniscient as the narrator knows her thoughts and feelings in part of the story.
The significance of the title is certainly heightened as the reader considers the point of view of Welty's narrative; the reader is privy to Phoenix's feelings all along her "worn path." Before she reaches this path and after she leaves it when arriving in Natchez, the point of view is third-person limited.
The exposition of the story is clearly in third-person narration as the weather is described and Phoenix Jackson is characterized in much the same matter-of-fact manner:

Her name was Phoenix Jackson. She was very old and small and she walked slowly in the dark pine shadows. . . Her eyes were blue with age. Her skin had a pattern of her own of numberless branching wrinkles and as though a whole little tree stood in the middle of her face.

If the reader learns Phoenix's thoughts at this point, it is because she speaks aloud:

The path ran up a hill. "Seem like there is chains about my feet, time I get this far," she said.

By paragraph 14, however, the narrator switches to omniscient as Phoenix is fully into the woods. The reader enters the old woman's imagination as "a little boy brought her a plate with a slice of marble cake on it."
Then, after Phoenix enters Natchez at the end of her journey of love, the narration switches back to third-person limited as the reader is closed off from Phoenix's interior monologue. Phoenix becomes silent; when the attendant who does not know her speaks to her, Phoenix does not respond. Because her thoughts are not revealed with omniscient narration, the reader can only surmise that this silence suggests Phoenix's defensiveness as she is in a white world in which she is vulnerable to being just put out the door by strangers. Fortunately, it appears her silence works for her, as a sympathetic nurse familiar with Phoenix hears the attendant raising her voice to the old woman. Under the pressure of the situation, and, perhaps, because she does not want the attendant to think she is being obstinate or rude, Phoenix still does not respond. When she does, she excuses herself,

My grandson. It was my memory had left me. There I sat and forgot why I made my long trip.

When the attendant who shouted at Phoenix later offers her "a few pennies," the old woman recognizes this condescension. She takes the money for her grandson, but not before winning a small victory:

"Five pennies is a nickel," said Phoenix stiffly."Here's a nickel," said the attendant.

Although the reader is closed off from the interior thoughts of Phoenix, this dialogue underscores the fact that Phoenix's mind is still quick at times as she manipulates the attendant into giving her a coin that makes her act of receiving seem less pitiful.