Money is withheld from participants' 401(k) accounts due to investment transfers directed by the participants. The money withheld is invested in a stable value fund within the 401(k) plan until it is remitted to the appropriate mutual fund company. (Money is remitted on a monthly or quarterly basis.)

What needs to be done with the interest earned on the participants' accounts during the time between the investment transfer and remittance to the mutual fund companies?

I presume you are talking about short term redemption fees that are withheld from the transfer amount. The money withheld is plan assets as are the earnings it receives while waiting to be sent to the mutual fund companies. The earnings should be allocated to participants. Depending on how the plan pays expenses, you could consider using it to offset expenses.