The correct option is C Walking on the beach
A participle is that form of the verb which partakes of the nature both of a Verb and of an Adjective.
A participle phrase will begin with a present or past participle. If the participle is present, it will dependably end in ing. Likewise a regular past participle will end in a consistent ed.
Since, all phrases require two or more words, a participle phrase will often include objects and/or modifiers that complete the thought.
Participle phrases always function as adjectives,adding description to the sentence.
In this case,
Option C is correct. The participle phrase, 'Walking on the beach' describes the noun 'Delores'. The present participle 'walking' introduces the participle phrase.
Options A, B and D are incorrect as they are devoid of any participle. 'Had been washed', 'dodged' are verbs and not participles.