All 3 Uses

pretense
in
Annexation
(Auto-generated)

It is wholly untrue, and unjust to ourselves, the pretence that the Annexation has been a measure of spoliation, unrightful and unrighteous—of military conquest under forms of peace and law—of territorial aggrandizement at the expense of justice, and justice due by a double sanctity to the weak.†

unconventional spelling: This is a British spelling. Americans use pretense.
We cannot too deeply regret the mismanagement which has disfigured the history of this question; and especially the neglect of the means which would have been so easy of satisfying even the unreasonable pretensions and the excited pride and passion of Mexico.†
*

pretensions = appearances or actions to help one pretend
The singular result has been produced, that while our neighbor has, in truth, no real right to blame or complain—when all the wrong is on her side, and there has been on ours a degree of delay and forbearance, in deference to her pretensions, which is to be paralleled by few precedents in the history of other nations—we have yet laid ourselves open to a great deal of denunciation hard to repel, and impossible to silence; and all history will carry it down as a certain fact, that Mexico would have declared war against us, and would have waged it seriously, if she had not been prevented by that very weakness which should have constituted her best defence.†

Definitions:

(1) (pretense)
a false appearance or action to help one pretend

This is sometimes seen in the expression "false pretense" or "false pretenses" which is just emphasizing that behavior or actions do not reflect the true situation.
(2) (meaning too rare to warrant focus)