Your money being saved, with a two-month history on that account, will not be frowned upon by any lender. As a smart saver, we all sort of earmark refunds, extra checks, etc. for budgets. That's totally fine.
Underwriters just look for stuff that doesn't make sense...people who normally have a $5k checking balance and suddenly balloon to $15k. It's that $10k that is in question. Gifts are allowed on many loan programs, they just need to be disclosed with a gift letter. Basically, just tell the lender what is happening and they rarely frown.
