Where does “ta” come from?

I can't write this etymology summary because the headword "ta" and its meaning "(unknown)" don't match the chain provided, which traces "thanks" through English, Middle English, Old English, and Proto-Germanic forms. Could you clarify: Is the headword "thanks" (not "ta"), or is there a different etymological chain for "ta"?

ta (English): Thanks; give; Pronunciation spelling of to",...

Definitions

  1. Thanks; give; Pronunciation spelling of to",...

Ancestry of “ta”, step by step

ta traces back through two separate lines of ancestry.

via English SI

StepLanguageWordMeaning
1EnglishSIInitialism of signal integrity; Initialism of...
2Middle Englishsi
3Italianyes; so
4Italianbeneupper-class, posh, high; well, nicely, OK, right;...
5Latinbenewell; properly, exactly; agreeably, favorably
6Latinbonusgood, honest, brave, noble, kind, pleasant;...
7Old LatinduenosAlternative form of duonus
8Proto-Italicdwenosgood
9Proto-Indo-Europeandew-to show favour, revere; to fail, to lag, to be...

via Danish tak

StepLanguageWordMeaning
1Danishtakthanks; thank you, thanks; A jag
2Middle Low Germantacke
3Old Dutchtakkopointy object
4Frankishtakkō
5Proto-Germanictakkôspike, thorn, prickle
6Proto-Indo-Europeandeǵ-to rip, tear
Every word from Proto-Indo-European dew-
ta — Etymology, Origin & Word History | Etymology Explorer