It’s just a mistake. The edition that you linked to says:

Initial text entry and proof-reading of this chapter were the work of volunteer Steven van Leeuwen.

The implication seems to be that the text was typed in by the volunteer, rather than starting with optical character recognition. Accidental insertion or duplication of a word is a common kind of error in text entry.

Here's a scan from the 1921 publication of the story in the collection Monday or Tuesday, showing that the original text lacked the extra “the”:

_{Virginia Woolf (1919). ‘Kew Gardens’. In Monday or Tuesday (1921), p. 70. Richmond: Hogarth Press.}

Other online editions don’t have the mistake, for example the Project Gutenberg edition is correct.

It’s just a mistake. The Celebration of Women Writers edition that you linked to says:

Initial text entry and proof-reading of this chapter were the work of volunteer Steven van Leeuwen.

The implication seems to be that the text was typed in by the volunteer, rather than starting with optical character recognition. (See the instructions that volunteers were given.) Accidental insertion or duplication of a word is a common kind of error in text entry.

Here's a scan from the 1921 publication of the story in the collection Monday or Tuesday, showing that the original text lacked the extra “the”:

_{Virginia Woolf (1919). ‘Kew Gardens’. In Monday or Tuesday (1921), p. 70. Richmond: Hogarth Press.}

The other online editions you found must have been copied from the Celebration of Women Writers edition. Copying is cheap and proof-reading is expensive. But not all online editions have the mistake, for example the Project Gutenberg edition is correct.