When we use the parallax method to find the distance of the stars "near" to earth..................?

The link you give refers to the local warping of space-time by local gravity. This is different from the "curvature" of the universe, which is too large-scale to affect parallax measurements. Gravitational deflection is very small unless the object is truly mive (galactic-core black hole, e.g.), and only affects very close alignment. The linked sketch is mively exaggerated. Deflection by our sun's gravity amounts to about 2 arc-seconds for a very close star. In short, the uncompensated effects of gravity on parallax measurement are negligible.