should the past participle agree in this sentence, "Elle s'est lavé les mains" ?

I have managed to find this which you should read,
https://www.lawlessfrench.com/grammar/agreement-with-pronominal-verbs/

You will note that Laura uses the following example: Elles se sont lavé les cheveux. Note that there is no agreement unless (like with avoir) the direct object precedes the auxilliary verb. The direct object is les cheveux, se becomes the indirect object.