You can call 311 or the Austin Animal Center to set up a surrender appointment. Try to give them as much information as possible so thst they can get the dogs adopted easier.
Have you posted to Craigslist, local lost and found sites such as Austin Lost and Found Pets or those specific to your area, also post on Nextdoor and if within Travis County you can file an online found report with 311. Most importantly have you had the dogs scanned for a microchip? It can be done at any vet's office without an appointment and it is free.
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