Does the HP warranty cover printer damage caused by using non-HP ink?

No, for the HP Smart Tank series, the warranty does not cover printer or printhead failure due to damage from use of non-HP ink or an expired printhead. In such cases, HP will charge its standard time and materials charges to service the printer or replace the printhead. (Page 2)

From the official HP Smart Tank 610 Wireless All-in-One manual, page 2

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