As Duncan says, 'sliver' is not the right terminology.
Without seeing the rest of the data, I would suggest selecting you main land body and then using select by location to select all features intersecting and within it.
Export your selection to a new feature, or switch selection and delete.
Hi Jota Us,
If your data is projected you could do a selection by Shape area greater than the "sliver" Island polygons, therefore selecting only the polygons you wish to keep and export the selection to a new feature. Preserving your original data. This also assumes that all the "slivers" are smaller in area than your study area.