Grudge

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late Middle English: variant of obsolete grutch ‘complain, murmur, grumble’, from Old French grouchier, of unknown origin. Compare with grouch.

wiktionary

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A variant of grutch (mid 15th-century, younger than begrudge), from Middle English grucchen(“to murmur, complain, feel envy, begrudge”), from Old French grouchier, groucier(“to murmur, grumble”) [1], of Germanic origin, akin to Middle High German grogezen(“to howl, wail”), German grocken(“to croak”). Compare also Old Norse krytja(“to murmur”), Old High German grunzen(“to grunt”).

etymonline

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grudge (v.)

mid-15c., "to murmur, complain," variant of grutch. Meaning "to begrudge, envy, wish to deprive of" is c. 1500. Related: Grudged; grudges; grudging; grudgingly.

grudge (n.)

"ill will excited by some special cause," late 15c., from grudge (v.).