so these boots make the wearer consider any plane he is at his native plane.
does it mean that an Eidolon who wear them can't be banished or dismissed with dismissal spells\effects?
Dismissal and banishment target extraplanar creatures, and with those boots an eidolon is not considered an extraplanar creature. Those two spells therefore can't target an eidolon wearing boots of planar grounding.
Spells which target outsiders or summoned creatures directly will still function. Devil snare and magic circle vs. whatever will work to ward areas, but the sending back to its home plane function of devil snare will fail due to the boots.
The wearer counts as being on their home plane anywhere, but they still have a home plane. Effects that only work on extraplanar creatures fail, but other effects referring to the wearer's home plane still work.
Further, a dispel magic on the boost followed by banishment would work. Though that could be said of practically anything.