Catherine Delahaye | Getty There's a shift going on with credit scores in the homebuying process that consumers may want to be aware of. Mortgage lenders are now permitted to use a credit score called VantageScore 4.0 as part of their underwriting process instead of a "classic" FICO score, which has been the only approved score for decades , government officials announced April 22. At some point in the coming months, another alternative score, FICO 10T, will also be permitted. The change applies to mortgages sold to Fannie Mae and Freddie Mac, government-sponsored enterprises that are the largest purchasers of mortgages on the secondary market. Additionally, the Federal Housing Administration, which insures many loans for first-time buyers, also will soon use these two scores, Housing and Urban Development Secretary Scott Turner said during a press conference announcing the changes. HUD oversees the FHA.…