If cells cannot visually inspect other cells, how do the cells of our immune system know if a particular cell they encounter is part of us or part of another organism?

Body recognizes the self cells and non-self cells by the help of the markers that is found on the cell.

Explanation:

The body has the ability to recognize the difference between the cells of the body and the cells that are not of our body.

The body recognizes the cells as self or non self. The cells of the body has coating made of glycoprotein which acts as the identifying markers for the cells of the body.

The blood type is one of the best example to encounter the self and non self cell. The body recognizes the blood of another person as another protein and considers it as antigen.