On the orders of King Dasharatha,ornaments were provided to Sita, before proceeding on exile.Sita accepted those ornaments to honor the sentiments of king Dasharatha.
राजा सत्वरम् आहूय व्यापृतम् वित्त संचये |
उवाच देश कालज्ञो निश्चितम् सर्वतः शुचि || २-३९-१४
The king, who knew what should be done at a proper place and time and was clear by all means, quickly called an officer placed in charge of the treasury and spoke in a decisive tone (as follows);-
वासांसि च महा अर्हाणि भूषणानि वराणि च |
वर्षाणि एतानि सम्ख्याय वैदेह्याः क्षिप्रम् आनय || २-३९-१५
"Quickly bring for Seetha, clothings of great worth and ornaments of high quality, taking into consideration all these years (that Seetha has to spend in exile)
नर इन्द्रेण एवम् उक्तः तु गत्वा कोश गृहम् ततः |
प्रायच्चत् सर्वम् आहृत्य सीतायै क्षिप्रम् एव तत् || २-३९-१६
After thus spoken by the king, the officer went to the treasury, brought all that in a lot and gave to Seetha.
सा सुजाता सुजातानि वैदेही प्रस्थिता वनम् |
भूषयाम् आस गात्राणि तैः विचित्रैः विभूषणैः || २-३९-१७
Setting out as she was to the forest, Seetha of noble birth adorned her beautiful limbs with those wonderful jewels.
In addition to the above,Maha Sati Anasuya also gave Sita ornaments ,during the meeting of Sri Rama with Maharishi Atri, at the latter’s hermitage ,
सा वस्त्रम् अन्ग रागम् च भूषणानि स्रजः तथा |
मैथिली प्रतिजग्राह प्रीति दानम् अनुत्तमम् || २-११८-२१
Seetha accepted the apparel, the scented cosmetic, the jewels and the garlands as unsurpassed gifts of love.
Reference: Book II : Ayodhya Kanda - Book Of Ayodhya
Chapter [Sarga] 39 and Chapter[Sarga]118.
Reference links:- (1)http://www.valmikiramayan.net/utf8/ayodhya/sarga39/ayodhya_39_frame.htm